3457 lines
164 KiB
Python
3457 lines
164 KiB
Python
# Guan is an open-source python package developed and maintained by https://www.guanjihuan.com/about. The primary location of this package is on website https://py.guanjihuan.com.
|
||
|
||
# With this package, you can calculate band structures, density of states, quantum transport and topological invariant of tight-binding models by invoking the functions you need. Other frequently used functions are also integrated in this package, such as file reading/writing, figure plotting, data processing.
|
||
|
||
# The current version is guan-0.0.170, updated on June 19, 2023.
|
||
|
||
# Installation: pip install --upgrade guan
|
||
|
||
# Modules:
|
||
|
||
# # Module 1: basic functions
|
||
# # Module 2: Fourier transform
|
||
# # Module 3: Hamiltonian of finite size systems
|
||
# # Module 4: Hamiltonian of models in the reciprocal space
|
||
# # Module 5: band structures and wave functions
|
||
# # Module 6: Green functions
|
||
# # Module 7: density of states
|
||
# # Module 8: quantum transport
|
||
# # Module 9: topological invariant
|
||
# # Module 10: read and write
|
||
# # Module 11: plot figures
|
||
# # Module 12: data processing
|
||
# # Module 13: file processing
|
||
# # Module 14: others
|
||
|
||
|
||
|
||
# import necessary packages
|
||
|
||
import numpy as np
|
||
import math
|
||
import cmath
|
||
import guan
|
||
|
||
|
||
|
||
# Module 1: basic functions
|
||
|
||
## test
|
||
|
||
def test():
|
||
print('\nSuccess in the installation of Guan package!\n')
|
||
|
||
## Pauli matrices
|
||
|
||
def sigma_0():
|
||
return np.eye(2)
|
||
|
||
def sigma_x():
|
||
return np.array([[0, 1],[1, 0]])
|
||
|
||
def sigma_y():
|
||
return np.array([[0, -1j],[1j, 0]])
|
||
|
||
def sigma_z():
|
||
return np.array([[1, 0],[0, -1]])
|
||
|
||
## Kronecker product of Pauli matrices
|
||
|
||
def sigma_00():
|
||
return np.kron(guan.sigma_0(), guan.sigma_0())
|
||
|
||
def sigma_0x():
|
||
return np.kron(guan.sigma_0(), guan.sigma_x())
|
||
|
||
def sigma_0y():
|
||
return np.kron(guan.sigma_0(), guan.sigma_y())
|
||
|
||
def sigma_0z():
|
||
return np.kron(guan.sigma_0(), guan.sigma_z())
|
||
|
||
def sigma_x0():
|
||
return np.kron(guan.sigma_x(), guan.sigma_0())
|
||
|
||
def sigma_xx():
|
||
return np.kron(guan.sigma_x(), guan.sigma_x())
|
||
|
||
def sigma_xy():
|
||
return np.kron(guan.sigma_x(), guan.sigma_y())
|
||
|
||
def sigma_xz():
|
||
return np.kron(guan.sigma_x(), guan.sigma_z())
|
||
|
||
def sigma_y0():
|
||
return np.kron(guan.sigma_y(), guan.sigma_0())
|
||
|
||
def sigma_yx():
|
||
return np.kron(guan.sigma_y(), guan.sigma_x())
|
||
|
||
def sigma_yy():
|
||
return np.kron(guan.sigma_y(), guan.sigma_y())
|
||
|
||
def sigma_yz():
|
||
return np.kron(guan.sigma_y(), guan.sigma_z())
|
||
|
||
def sigma_z0():
|
||
return np.kron(guan.sigma_z(), guan.sigma_0())
|
||
|
||
def sigma_zx():
|
||
return np.kron(guan.sigma_z(), guan.sigma_x())
|
||
|
||
def sigma_zy():
|
||
return np.kron(guan.sigma_z(), guan.sigma_y())
|
||
|
||
def sigma_zz():
|
||
return np.kron(guan.sigma_z(), guan.sigma_z())
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 2: Fourier_transform
|
||
|
||
# Fourier transform for discrete lattices
|
||
|
||
# 通过元胞和跃迁项得到一维的哈密顿量（需要输入k值）
|
||
def one_dimensional_fourier_transform(k, unit_cell, hopping):
|
||
unit_cell = np.array(unit_cell)
|
||
hopping = np.array(hopping)
|
||
hamiltonian = unit_cell+hopping*cmath.exp(1j*k)+hopping.transpose().conj()*cmath.exp(-1j*k)
|
||
return hamiltonian
|
||
|
||
# 通过元胞和跃迁项得到二维方格子的哈密顿量（需要输入k值）
|
||
def two_dimensional_fourier_transform_for_square_lattice(k1, k2, unit_cell, hopping_1, hopping_2):
|
||
unit_cell = np.array(unit_cell)
|
||
hopping_1 = np.array(hopping_1)
|
||
hopping_2 = np.array(hopping_2)
|
||
hamiltonian = unit_cell+hopping_1*cmath.exp(1j*k1)+hopping_1.transpose().conj()*cmath.exp(-1j*k1)+hopping_2*cmath.exp(1j*k2)+hopping_2.transpose().conj()*cmath.exp(-1j*k2)
|
||
return hamiltonian
|
||
|
||
# 通过元胞和跃迁项得到三维立方格子的哈密顿量（需要输入k值）
|
||
def three_dimensional_fourier_transform_for_cubic_lattice(k1, k2, k3, unit_cell, hopping_1, hopping_2, hopping_3):
|
||
unit_cell = np.array(unit_cell)
|
||
hopping_1 = np.array(hopping_1)
|
||
hopping_2 = np.array(hopping_2)
|
||
hopping_3 = np.array(hopping_3)
|
||
hamiltonian = unit_cell+hopping_1*cmath.exp(1j*k1)+hopping_1.transpose().conj()*cmath.exp(-1j*k1)+hopping_2*cmath.exp(1j*k2)+hopping_2.transpose().conj()*cmath.exp(-1j*k2)+hopping_3*cmath.exp(1j*k3)+hopping_3.transpose().conj()*cmath.exp(-1j*k3)
|
||
return hamiltonian
|
||
|
||
# 通过元胞和跃迁项得到一维的哈密顿量（返回的哈密顿量为携带k的函数）
|
||
def one_dimensional_fourier_transform_with_k(unit_cell, hopping):
|
||
import functools
|
||
hamiltonian_function = functools.partial(guan.one_dimensional_fourier_transform, unit_cell=unit_cell, hopping=hopping)
|
||
return hamiltonian_function
|
||
|
||
# 通过元胞和跃迁项得到二维方格子的哈密顿量（返回的哈密顿量为携带k的函数）
|
||
def two_dimensional_fourier_transform_for_square_lattice_with_k1_k2(unit_cell, hopping_1, hopping_2):
|
||
import functools
|
||
hamiltonian_function = functools.partial(guan.two_dimensional_fourier_transform_for_square_lattice, unit_cell=unit_cell, hopping_1=hopping_1, hopping_2=hopping_2)
|
||
return hamiltonian_function
|
||
|
||
# 通过元胞和跃迁项得到三维立方格子的哈密顿量（返回的哈密顿量为携带k的函数）
|
||
def three_dimensional_fourier_transform_for_cubic_lattice_with_k1_k2_k3(unit_cell, hopping_1, hopping_2, hopping_3):
|
||
import functools
|
||
hamiltonian_function = functools.partial(guan.three_dimensional_fourier_transform_for_cubic_lattice, unit_cell=unit_cell, hopping_1=hopping_1, hopping_2=hopping_2, hopping_3=hopping_3)
|
||
return hamiltonian_function
|
||
|
||
## calculate reciprocal lattice vectors
|
||
|
||
# 由实空间格矢得到倒空间格矢（一维）
|
||
def calculate_one_dimensional_reciprocal_lattice_vector(a1):
|
||
b1 = 2*np.pi/a1
|
||
return b1
|
||
|
||
# 由实空间格矢得到倒空间格矢（二维）
|
||
def calculate_two_dimensional_reciprocal_lattice_vectors(a1, a2):
|
||
a1 = np.array(a1)
|
||
a2 = np.array(a2)
|
||
a1 = np.append(a1, 0)
|
||
a2 = np.append(a2, 0)
|
||
a3 = np.array([0, 0, 1])
|
||
b1 = 2*np.pi*np.cross(a2, a3)/np.dot(a1, np.cross(a2, a3))
|
||
b2 = 2*np.pi*np.cross(a3, a1)/np.dot(a1, np.cross(a2, a3))
|
||
b1 = np.delete(b1, 2)
|
||
b2 = np.delete(b2, 2)
|
||
return b1, b2
|
||
|
||
# 由实空间格矢得到倒空间格矢（三维）
|
||
def calculate_three_dimensional_reciprocal_lattice_vectors(a1, a2, a3):
|
||
a1 = np.array(a1)
|
||
a2 = np.array(a2)
|
||
a3 = np.array(a3)
|
||
b1 = 2*np.pi*np.cross(a2, a3)/np.dot(a1, np.cross(a2, a3))
|
||
b2 = 2*np.pi*np.cross(a3, a1)/np.dot(a1, np.cross(a2, a3))
|
||
b3 = 2*np.pi*np.cross(a1, a2)/np.dot(a1, np.cross(a2, a3))
|
||
return b1, b2, b3
|
||
|
||
# 由实空间格矢得到倒空间格矢（一维），这里为符号运算
|
||
def calculate_one_dimensional_reciprocal_lattice_vector_with_sympy(a1):
|
||
import sympy
|
||
b1 = 2*sympy.pi/a1
|
||
return b1
|
||
|
||
# 由实空间格矢得到倒空间格矢（二维），这里为符号运算
|
||
def calculate_two_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2):
|
||
import sympy
|
||
a1 = sympy.Matrix(1, 3, [a1[0], a1[1], 0])
|
||
a2 = sympy.Matrix(1, 3, [a2[0], a2[1], 0])
|
||
a3 = sympy.Matrix(1, 3, [0, 0, 1])
|
||
cross_a2_a3 = a2.cross(a3)
|
||
cross_a3_a1 = a3.cross(a1)
|
||
b1 = 2*sympy.pi*cross_a2_a3/a1.dot(cross_a2_a3)
|
||
b2 = 2*sympy.pi*cross_a3_a1/a1.dot(cross_a2_a3)
|
||
b1 = sympy.Matrix(1, 2, [b1[0], b1[1]])
|
||
b2 = sympy.Matrix(1, 2, [b2[0], b2[1]])
|
||
return b1, b2
|
||
|
||
# 由实空间格矢得到倒空间格矢（三维），这里为符号运算
|
||
def calculate_three_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2, a3):
|
||
import sympy
|
||
cross_a2_a3 = a2.cross(a3)
|
||
cross_a3_a1 = a3.cross(a1)
|
||
cross_a1_a2 = a1.cross(a2)
|
||
b1 = 2*sympy.pi*cross_a2_a3/a1.dot(cross_a2_a3)
|
||
b2 = 2*sympy.pi*cross_a3_a1/a1.dot(cross_a2_a3)
|
||
b3 = 2*sympy.pi*cross_a1_a2/a1.dot(cross_a2_a3)
|
||
return b1, b2, b3
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 3: Hamiltonian of finite size systems
|
||
|
||
# 构建一维的有限尺寸体系哈密顿量（可设置是否为周期边界条件）
|
||
def hamiltonian_of_finite_size_system_along_one_direction(N, on_site=0, hopping=1, period=0):
|
||
on_site = np.array(on_site)
|
||
hopping = np.array(hopping)
|
||
if on_site.shape==():
|
||
dim = 1
|
||
else:
|
||
dim = on_site.shape[0]
|
||
hamiltonian = np.zeros((N*dim, N*dim), dtype=complex)
|
||
for i0 in range(N):
|
||
hamiltonian[i0*dim+0:i0*dim+dim, i0*dim+0:i0*dim+dim] = on_site
|
||
for i0 in range(N-1):
|
||
hamiltonian[i0*dim+0:i0*dim+dim, (i0+1)*dim+0:(i0+1)*dim+dim] = hopping
|
||
hamiltonian[(i0+1)*dim+0:(i0+1)*dim+dim, i0*dim+0:i0*dim+dim] = hopping.transpose().conj()
|
||
if period == 1:
|
||
hamiltonian[(N-1)*dim+0:(N-1)*dim+dim, 0:dim] = hopping
|
||
hamiltonian[0:dim, (N-1)*dim+0:(N-1)*dim+dim] = hopping.transpose().conj()
|
||
return hamiltonian
|
||
|
||
# 构建二维的方格子有限尺寸体系哈密顿量（可设置是否为周期边界条件）
|
||
def hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1, N2, on_site=0, hopping_1=1, hopping_2=1, period_1=0, period_2=0):
|
||
on_site = np.array(on_site)
|
||
hopping_1 = np.array(hopping_1)
|
||
hopping_2 = np.array(hopping_2)
|
||
if on_site.shape==():
|
||
dim = 1
|
||
else:
|
||
dim = on_site.shape[0]
|
||
hamiltonian = np.zeros((N1*N2*dim, N1*N2*dim), dtype=complex)
|
||
for i1 in range(N1):
|
||
for i2 in range(N2):
|
||
hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = on_site
|
||
for i1 in range(N1-1):
|
||
for i2 in range(N2):
|
||
hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, (i1+1)*N2*dim+i2*dim+0:(i1+1)*N2*dim+i2*dim+dim] = hopping_1
|
||
hamiltonian[(i1+1)*N2*dim+i2*dim+0:(i1+1)*N2*dim+i2*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = hopping_1.transpose().conj()
|
||
for i1 in range(N1):
|
||
for i2 in range(N2-1):
|
||
hamiltonian[i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim, i1*N2*dim+(i2+1)*dim+0:i1*N2*dim+(i2+1)*dim+dim] = hopping_2
|
||
hamiltonian[i1*N2*dim+(i2+1)*dim+0:i1*N2*dim+(i2+1)*dim+dim, i1*N2*dim+i2*dim+0:i1*N2*dim+i2*dim+dim] = hopping_2.transpose().conj()
|
||
if period_1 == 1:
|
||
for i2 in range(N2):
|
||
hamiltonian[(N1-1)*N2*dim+i2*dim+0:(N1-1)*N2*dim+i2*dim+dim, i2*dim+0:i2*dim+dim] = hopping_1
|
||
hamiltonian[i2*dim+0:i2*dim+dim, (N1-1)*N2*dim+i2*dim+0:(N1-1)*N2*dim+i2*dim+dim] = hopping_1.transpose().conj()
|
||
if period_2 == 1:
|
||
for i1 in range(N1):
|
||
hamiltonian[i1*N2*dim+(N2-1)*dim+0:i1*N2*dim+(N2-1)*dim+dim, i1*N2*dim+0:i1*N2*dim+dim] = hopping_2
|
||
hamiltonian[i1*N2*dim+0:i1*N2*dim+dim, i1*N2*dim+(N2-1)*dim+0:i1*N2*dim+(N2-1)*dim+dim] = hopping_2.transpose().conj()
|
||
return hamiltonian
|
||
|
||
# 构建三维的立方格子有限尺寸体系哈密顿量（可设置是否为周期边界条件）
|
||
def hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(N1, N2, N3, on_site=0, hopping_1=1, hopping_2=1, hopping_3=1, period_1=0, period_2=0, period_3=0):
|
||
on_site = np.array(on_site)
|
||
hopping_1 = np.array(hopping_1)
|
||
hopping_2 = np.array(hopping_2)
|
||
hopping_3 = np.array(hopping_3)
|
||
if on_site.shape==():
|
||
dim = 1
|
||
else:
|
||
dim = on_site.shape[0]
|
||
hamiltonian = np.zeros((N1*N2*N3*dim, N1*N2*N3*dim), dtype=complex)
|
||
for i1 in range(N1):
|
||
for i2 in range(N2):
|
||
for i3 in range(N3):
|
||
hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = on_site
|
||
for i1 in range(N1-1):
|
||
for i2 in range(N2):
|
||
for i3 in range(N3):
|
||
hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, (i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1
|
||
hamiltonian[(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(i1+1)*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1.transpose().conj()
|
||
for i1 in range(N1):
|
||
for i2 in range(N2-1):
|
||
for i3 in range(N3):
|
||
hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+dim] = hopping_2
|
||
hamiltonian[i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(i2+1)*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_2.transpose().conj()
|
||
for i1 in range(N1):
|
||
for i2 in range(N2):
|
||
for i3 in range(N3-1):
|
||
hamiltonian[i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim, i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+dim] = hopping_3
|
||
hamiltonian[i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(i3+1)*dim+dim, i1*N2*N3*dim+i2*N3*dim+i3*dim+0:i1*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_3.transpose().conj()
|
||
if period_1 == 1:
|
||
for i2 in range(N2):
|
||
for i3 in range(N3):
|
||
hamiltonian[(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+dim, i2*N3*dim+i3*dim+0:i2*N3*dim+i3*dim+dim] = hopping_1
|
||
hamiltonian[i2*N3*dim+i3*dim+0:i2*N3*dim+i3*dim+dim, (N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+0:(N1-1)*N2*N3*dim+i2*N3*dim+i3*dim+dim] = hopping_1.transpose().conj()
|
||
if period_2 == 1:
|
||
for i1 in range(N1):
|
||
for i3 in range(N3):
|
||
hamiltonian[i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+dim, i1*N2*N3*dim+i3*dim+0:i1*N2*N3*dim+i3*dim+dim] = hopping_2
|
||
hamiltonian[i1*N2*N3*dim+i3*dim+0:i1*N2*N3*dim+i3*dim+dim, i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+0:i1*N2*N3*dim+(N2-1)*N3*dim+i3*dim+dim] = hopping_2.transpose().conj()
|
||
if period_3 == 1:
|
||
for i1 in range(N1):
|
||
for i2 in range(N2):
|
||
hamiltonian[i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+dim, i1*N2*N3*dim+i2*N3*dim+0:i1*N2*N3*dim+i2*N3*dim+dim] = hopping_3
|
||
hamiltonian[i1*N2*N3*dim+i2*N3*dim+0:i1*N2*N3*dim+i2*N3*dim+dim, i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+0:i1*N2*N3*dim+i2*N3*dim+(N3-1)*dim+dim] = hopping_3.transpose().conj()
|
||
return hamiltonian
|
||
|
||
# 构建有限尺寸的SSH模型哈密顿量
|
||
def hamiltonian_of_finite_size_ssh_model(N, v=0.6, w=1, onsite_1=0, onsite_2=0, period=1):
|
||
hamiltonian = np.zeros((2*N, 2*N))
|
||
for i in range(N):
|
||
hamiltonian[i*2+0, i*2+0] = onsite_1
|
||
hamiltonian[i*2+1, i*2+1] = onsite_2
|
||
hamiltonian[i*2+0, i*2+1] = v
|
||
hamiltonian[i*2+1, i*2+0] = v
|
||
for i in range(N-1):
|
||
hamiltonian[i*2+1, (i+1)*2+0] = w
|
||
hamiltonian[(i+1)*2+0, i*2+1] = w
|
||
if period==1:
|
||
hamiltonian[0, 2*N-1] = w
|
||
hamiltonian[2*N-1, 0] = w
|
||
return hamiltonian
|
||
|
||
# 获取Zigzag边的石墨烯条带的元胞间跃迁
|
||
def get_hopping_term_of_graphene_ribbon_along_zigzag_direction(N, eta=0):
|
||
hopping = np.zeros((4*N, 4*N), dtype=complex)
|
||
for i0 in range(N):
|
||
hopping[4*i0+0, 4*i0+0] = eta
|
||
hopping[4*i0+1, 4*i0+1] = eta
|
||
hopping[4*i0+2, 4*i0+2] = eta
|
||
hopping[4*i0+3, 4*i0+3] = eta
|
||
hopping[4*i0+1, 4*i0+0] = 1
|
||
hopping[4*i0+2, 4*i0+3] = 1
|
||
return hopping
|
||
|
||
# 构建有限尺寸的石墨烯哈密顿量（可设置是否为周期边界条件）
|
||
def hamiltonian_of_finite_size_system_along_two_directions_for_graphene(N1, N2, period_1=0, period_2=0):
|
||
on_site = guan.hamiltonian_of_finite_size_system_along_one_direction(4)
|
||
hopping_1 = guan.get_hopping_term_of_graphene_ribbon_along_zigzag_direction(1)
|
||
hopping_2 = np.zeros((4, 4), dtype=complex)
|
||
hopping_2[3, 0] = 1
|
||
hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1, N2, on_site, hopping_1, hopping_2, period_1, period_2)
|
||
return hamiltonian
|
||
|
||
# 获取石墨烯有效模型沿着x方向的在位能和跃迁项（其中，动量qy为参数）
|
||
def get_onsite_and_hopping_terms_of_2d_effective_graphene_along_one_direction(qy, t=1, staggered_potential=0, eta=0, valley_index=0):
|
||
constant = -np.sqrt(3)/2
|
||
h00 = np.zeros((2, 2), dtype=complex)
|
||
h00[0, 0] = staggered_potential
|
||
h00[1, 1] = -staggered_potential
|
||
h00[0, 1] = -1j*constant*t*np.sin(qy)
|
||
h00[1, 0] = 1j*constant*t*np.sin(qy)
|
||
h01 = np.zeros((2, 2), dtype=complex)
|
||
h01[0, 0] = eta
|
||
h01[1, 1] = eta
|
||
if valley_index == 0:
|
||
h01[0, 1] = constant*t*(-1j/2)
|
||
h01[1, 0] = constant*t*(-1j/2)
|
||
else:
|
||
h01[0, 1] = constant*t*(1j/2)
|
||
h01[1, 0] = constant*t*(1j/2)
|
||
return h00, h01
|
||
|
||
# 获取BHZ模型的在位能和跃迁项
|
||
def get_onsite_and_hopping_terms_of_bhz_model(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1):
|
||
E_s = C+M-4*(D+B)/(a**2)
|
||
E_p = C-M-4*(D-B)/(a**2)
|
||
V_ss = (D+B)/(a**2)
|
||
V_pp = (D-B)/(a**2)
|
||
V_sp = -1j*A/(2*a)
|
||
H0 = np.zeros((4, 4), dtype=complex)
|
||
H1 = np.zeros((4, 4), dtype=complex)
|
||
H2 = np.zeros((4, 4), dtype=complex)
|
||
H0[0, 0] = E_s
|
||
H0[1, 1] = E_p
|
||
H0[2, 2] = E_s
|
||
H0[3, 3] = E_p
|
||
H1[0, 0] = V_ss
|
||
H1[1, 1] = V_pp
|
||
H1[2, 2] = V_ss
|
||
H1[3, 3] = V_pp
|
||
H1[0, 1] = V_sp
|
||
H1[1, 0] = -np.conj(V_sp)
|
||
H1[2, 3] = np.conj(V_sp)
|
||
H1[3, 2] = -V_sp
|
||
H2[0, 0] = V_ss
|
||
H2[1, 1] = V_pp
|
||
H2[2, 2] = V_ss
|
||
H2[3, 3] = V_pp
|
||
H2[0, 1] = 1j*V_sp
|
||
H2[1, 0] = 1j*np.conj(V_sp)
|
||
H2[2, 3] = -1j*np.conj(V_sp)
|
||
H2[3, 2] = -1j*V_sp
|
||
return H0, H1, H2
|
||
|
||
# 获取半个BHZ模型的在位能和跃迁项（自旋向上）
|
||
def get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_up(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1):
|
||
E_s = C+M-4*(D+B)/(a**2)
|
||
E_p = C-M-4*(D-B)/(a**2)
|
||
V_ss = (D+B)/(a**2)
|
||
V_pp = (D-B)/(a**2)
|
||
V_sp = -1j*A/(2*a)
|
||
H0 = np.zeros((2, 2), dtype=complex)
|
||
H1 = np.zeros((2, 2), dtype=complex)
|
||
H2 = np.zeros((2, 2), dtype=complex)
|
||
H0[0, 0] = E_s
|
||
H0[1, 1] = E_p
|
||
H1[0, 0] = V_ss
|
||
H1[1, 1] = V_pp
|
||
H1[0, 1] = V_sp
|
||
H1[1, 0] = -np.conj(V_sp)
|
||
H2[0, 0] = V_ss
|
||
H2[1, 1] = V_pp
|
||
H2[0, 1] = 1j*V_sp
|
||
H2[1, 0] = 1j*np.conj(V_sp)
|
||
return H0, H1, H2
|
||
|
||
# 获取半个BHZ模型的在位能和跃迁项（自旋向下）
|
||
def get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_down(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1):
|
||
E_s = C+M-4*(D+B)/(a**2)
|
||
E_p = C-M-4*(D-B)/(a**2)
|
||
V_ss = (D+B)/(a**2)
|
||
V_pp = (D-B)/(a**2)
|
||
V_sp = -1j*A/(2*a)
|
||
H0 = np.zeros((2, 2), dtype=complex)
|
||
H1 = np.zeros((2, 2), dtype=complex)
|
||
H2 = np.zeros((2, 2), dtype=complex)
|
||
H0[0, 0] = E_s
|
||
H0[1, 1] = E_p
|
||
H1[0, 0] = V_ss
|
||
H1[1, 1] = V_pp
|
||
H1[0, 1] = np.conj(V_sp)
|
||
H1[1, 0] = -V_sp
|
||
H2[0, 0] = V_ss
|
||
H2[1, 1] = V_pp
|
||
H2[0, 1] = -1j*np.conj(V_sp)
|
||
H2[1, 0] = -1j*V_sp
|
||
return H0, H1, H2
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 4: Hamiltonian of models in the reciprocal space
|
||
|
||
# 一维链的哈密顿量
|
||
def hamiltonian_of_simple_chain(k):
|
||
hamiltonian = guan.one_dimensional_fourier_transform(k, unit_cell=0, hopping=1)
|
||
return hamiltonian
|
||
|
||
# 二维方格子的哈密顿量
|
||
def hamiltonian_of_square_lattice(k1, k2):
|
||
hamiltonian = guan.two_dimensional_fourier_transform_for_square_lattice(k1, k2, unit_cell=0, hopping_1=1, hopping_2=1)
|
||
return hamiltonian
|
||
|
||
# 准一维方格子条带的哈密顿量
|
||
def hamiltonian_of_square_lattice_in_quasi_one_dimension(k, N=10, period=0):
|
||
h00 = np.zeros((N, N), dtype=complex) # hopping in a unit cell
|
||
h01 = np.zeros((N, N), dtype=complex) # hopping between unit cells
|
||
for i in range(N-1):
|
||
h00[i, i+1] = 1
|
||
h00[i+1, i] = 1
|
||
if period == 1:
|
||
h00[N-1, 0] = 1
|
||
h00[0, N-1] = 1
|
||
for i in range(N):
|
||
h01[i, i] = 1
|
||
hamiltonian = guan.one_dimensional_fourier_transform(k, unit_cell=h00, hopping=h01)
|
||
return hamiltonian
|
||
|
||
# 三维立方格子的哈密顿量
|
||
def hamiltonian_of_cubic_lattice(k1, k2, k3):
|
||
hamiltonian = guan.three_dimensional_fourier_transform_for_cubic_lattice(k1, k2, k3, unit_cell=0, hopping_1=1, hopping_2=1, hopping_3=1)
|
||
return hamiltonian
|
||
|
||
# SSH模型的哈密顿量
|
||
def hamiltonian_of_ssh_model(k, v=0.6, w=1):
|
||
hamiltonian = np.zeros((2, 2), dtype=complex)
|
||
hamiltonian[0,1] = v+w*cmath.exp(-1j*k)
|
||
hamiltonian[1,0] = v+w*cmath.exp(1j*k)
|
||
return hamiltonian
|
||
|
||
# 石墨烯的哈密顿量
|
||
def hamiltonian_of_graphene(k1, k2, staggered_potential=0, t=1, a=1/math.sqrt(3)):
|
||
h0 = np.zeros((2, 2), dtype=complex) # mass term
|
||
h1 = np.zeros((2, 2), dtype=complex) # nearest hopping
|
||
h0[0, 0] = staggered_potential
|
||
h0[1, 1] = -staggered_potential
|
||
h1[1, 0] = t*(cmath.exp(1j*k2*a)+cmath.exp(1j*math.sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a-1j/2*k2*a))
|
||
h1[0, 1] = h1[1, 0].conj()
|
||
hamiltonian = h0 + h1
|
||
return hamiltonian
|
||
|
||
# 石墨烯有效模型的哈密顿量
|
||
def effective_hamiltonian_of_graphene(qx, qy, t=1, staggered_potential=0, valley_index=0):
|
||
hamiltonian = np.zeros((2, 2), dtype=complex)
|
||
hamiltonian[0, 0] = staggered_potential
|
||
hamiltonian[1, 1] = -staggered_potential
|
||
constant = -np.sqrt(3)/2
|
||
if valley_index == 0:
|
||
hamiltonian[0, 1] = constant*t*(qx-1j*qy)
|
||
hamiltonian[1, 0] = constant*t*(qx+1j*qy)
|
||
else:
|
||
hamiltonian[0, 1] = constant*t*(-qx-1j*qy)
|
||
hamiltonian[1, 0] = constant*t*(-qx+1j*qy)
|
||
return hamiltonian
|
||
|
||
# 石墨烯有效模型离散化后的哈密顿量
|
||
def effective_hamiltonian_of_graphene_after_discretization(qx, qy, t=1, staggered_potential=0, valley_index=0):
|
||
hamiltonian = np.zeros((2, 2), dtype=complex)
|
||
hamiltonian[0, 0] = staggered_potential
|
||
hamiltonian[1, 1] = -staggered_potential
|
||
constant = -np.sqrt(3)/2
|
||
if valley_index == 0:
|
||
hamiltonian[0, 1] = constant*t*(np.sin(qx)-1j*np.sin(qy))
|
||
hamiltonian[1, 0] = constant*t*(np.sin(qx)+1j*np.sin(qy))
|
||
else:
|
||
hamiltonian[0, 1] = constant*t*(-np.sin(qx)-1j*np.sin(qy))
|
||
hamiltonian[1, 0] = constant*t*(-np.sin(qx)+1j*np.sin(qy))
|
||
return hamiltonian
|
||
|
||
# 准一维Zigzag边石墨烯条带的哈密顿量
|
||
def hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension(k, N=10, M=0, t=1, period=0):
|
||
h00 = np.zeros((4*N, 4*N), dtype=complex) # hopping in a unit cell
|
||
h01 = np.zeros((4*N, 4*N), dtype=complex) # hopping between unit cells
|
||
for i in range(N):
|
||
h00[i*4+0, i*4+0] = M
|
||
h00[i*4+1, i*4+1] = -M
|
||
h00[i*4+2, i*4+2] = M
|
||
h00[i*4+3, i*4+3] = -M
|
||
h00[i*4+0, i*4+1] = t
|
||
h00[i*4+1, i*4+0] = t
|
||
h00[i*4+1, i*4+2] = t
|
||
h00[i*4+2, i*4+1] = t
|
||
h00[i*4+2, i*4+3] = t
|
||
h00[i*4+3, i*4+2] = t
|
||
for i in range(N-1):
|
||
h00[i*4+3, (i+1)*4+0] = t
|
||
h00[(i+1)*4+0, i*4+3] = t
|
||
if period == 1:
|
||
h00[(N-1)*4+3, 0] = t
|
||
h00[0, (N-1)*4+3] = t
|
||
for i in range(N):
|
||
h01[i*4+1, i*4+0] = t
|
||
h01[i*4+2, i*4+3] = t
|
||
hamiltonian = guan.one_dimensional_fourier_transform(k, unit_cell=h00, hopping=h01)
|
||
return hamiltonian
|
||
|
||
# Haldane模型的哈密顿量
|
||
def hamiltonian_of_haldane_model(k1, k2, M=2/3, t1=1, t2=1/3, phi=math.pi/4, a=1/math.sqrt(3)):
|
||
h0 = np.zeros((2, 2), dtype=complex) # mass term
|
||
h1 = np.zeros((2, 2), dtype=complex) # nearest hopping
|
||
h2 = np.zeros((2, 2), dtype=complex) # next nearest hopping
|
||
h0[0, 0] = M
|
||
h0[1, 1] = -M
|
||
h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*math.sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a-1j/2*k2*a))
|
||
h1[0, 1] = h1[1, 0].conj()
|
||
h2[0, 0] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*math.sqrt(3)*k1*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a-1j*3/2*k2*a))
|
||
h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*math.sqrt(3)*k1*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*math.sqrt(3)/2*k1*a-1j*3/2*k2*a))
|
||
hamiltonian = h0 + h1 + h2 + h2.transpose().conj()
|
||
return hamiltonian
|
||
|
||
# 准一维Haldane模型条带的哈密顿量
|
||
def hamiltonian_of_haldane_model_in_quasi_one_dimension(k, N=10, M=2/3, t1=1, t2=1/3, phi=math.pi/4, period=0):
|
||
h00 = np.zeros((4*N, 4*N), dtype=complex) # hopping in a unit cell
|
||
h01 = np.zeros((4*N, 4*N), dtype=complex) # hopping between unit cells
|
||
for i in range(N):
|
||
h00[i*4+0, i*4+0] = M
|
||
h00[i*4+1, i*4+1] = -M
|
||
h00[i*4+2, i*4+2] = M
|
||
h00[i*4+3, i*4+3] = -M
|
||
h00[i*4+0, i*4+1] = t1
|
||
h00[i*4+1, i*4+0] = t1
|
||
h00[i*4+1, i*4+2] = t1
|
||
h00[i*4+2, i*4+1] = t1
|
||
h00[i*4+2, i*4+3] = t1
|
||
h00[i*4+3, i*4+2] = t1
|
||
h00[i*4+0, i*4+2] = t2*cmath.exp(-1j*phi)
|
||
h00[i*4+2, i*4+0] = h00[i*4+0, i*4+2].conj()
|
||
h00[i*4+1, i*4+3] = t2*cmath.exp(-1j*phi)
|
||
h00[i*4+3, i*4+1] = h00[i*4+1, i*4+3].conj()
|
||
for i in range(N-1):
|
||
h00[i*4+3, (i+1)*4+0] = t1
|
||
h00[(i+1)*4+0, i*4+3] = t1
|
||
h00[i*4+2, (i+1)*4+0] = t2*cmath.exp(1j*phi)
|
||
h00[(i+1)*4+0, i*4+2] = h00[i*4+2, (i+1)*4+0].conj()
|
||
h00[i*4+3, (i+1)*4+1] = t2*cmath.exp(1j*phi)
|
||
h00[(i+1)*4+1, i*4+3] = h00[i*4+3, (i+1)*4+1].conj()
|
||
if period == 1:
|
||
h00[(N-1)*4+3, 0] = t1
|
||
h00[0, (N-1)*4+3] = t1
|
||
h00[(N-1)*4+2, 0] = t2*cmath.exp(1j*phi)
|
||
h00[0, (N-1)*4+2] = h00[(N-1)*4+2, 0].conj()
|
||
h00[(N-1)*4+3, 1] = t2*cmath.exp(1j*phi)
|
||
h00[1, (N-1)*4+3] = h00[(N-1)*4+3, 1].conj()
|
||
for i in range(N):
|
||
h01[i*4+1, i*4+0] = t1
|
||
h01[i*4+2, i*4+3] = t1
|
||
h01[i*4+0, i*4+0] = t2*cmath.exp(1j*phi)
|
||
h01[i*4+1, i*4+1] = t2*cmath.exp(-1j*phi)
|
||
h01[i*4+2, i*4+2] = t2*cmath.exp(1j*phi)
|
||
h01[i*4+3, i*4+3] = t2*cmath.exp(-1j*phi)
|
||
h01[i*4+1, i*4+3] = t2*cmath.exp(1j*phi)
|
||
h01[i*4+2, i*4+0] = t2*cmath.exp(-1j*phi)
|
||
if i != 0:
|
||
h01[i*4+1, (i-1)*4+3] = t2*cmath.exp(1j*phi)
|
||
for i in range(N-1):
|
||
h01[i*4+2, (i+1)*4+0] = t2*cmath.exp(-1j*phi)
|
||
hamiltonian = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
|
||
return hamiltonian
|
||
|
||
# 一个量子反常霍尔效应的哈密顿量
|
||
def hamiltonian_of_one_QAH_model(k1, k2, t1=1, t2=1, t3=0.5, m=-1):
|
||
hamiltonian = np.zeros((2, 2), dtype=complex)
|
||
hamiltonian[0, 1] = 2*t1*math.cos(k1)-1j*2*t1*math.cos(k2)
|
||
hamiltonian[1, 0] = 2*t1*math.cos(k1)+1j*2*t1*math.cos(k2)
|
||
hamiltonian[0, 0] = m+2*t3*math.sin(k1)+2*t3*math.sin(k2)+2*t2*math.cos(k1+k2)
|
||
hamiltonian[1, 1] = -(m+2*t3*math.sin(k1)+2*t3*math.sin(k2)+2*t2*math.cos(k1+k2))
|
||
return hamiltonian
|
||
|
||
# BHZ模型的哈密顿量
|
||
def hamiltonian_of_bhz_model(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01):
|
||
hamiltonian = np.zeros((4, 4), dtype=complex)
|
||
varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky))
|
||
d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky))
|
||
d1_d2 = A*(math.sin(kx)+1j*math.sin(ky))
|
||
hamiltonian[0, 0] = varepsilon+d3
|
||
hamiltonian[1, 1] = varepsilon-d3
|
||
hamiltonian[0, 1] = np.conj(d1_d2)
|
||
hamiltonian[1, 0] = d1_d2
|
||
hamiltonian[2, 2] = varepsilon+d3
|
||
hamiltonian[3, 3] = varepsilon-d3
|
||
hamiltonian[2, 3] = -d1_d2
|
||
hamiltonian[3, 2] = -np.conj(d1_d2)
|
||
return hamiltonian
|
||
|
||
# 半BHZ模型的哈密顿量（自旋向上）
|
||
def hamiltonian_of_half_bhz_model_for_spin_up(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01):
|
||
hamiltonian = np.zeros((2, 2), dtype=complex)
|
||
varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky))
|
||
d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky))
|
||
d1_d2 = A*(math.sin(kx)+1j*math.sin(ky))
|
||
hamiltonian[0, 0] = varepsilon+d3
|
||
hamiltonian[1, 1] = varepsilon-d3
|
||
hamiltonian[0, 1] = np.conj(d1_d2)
|
||
hamiltonian[1, 0] = d1_d2
|
||
return hamiltonian
|
||
|
||
# 半BHZ模型的哈密顿量（自旋向下）
|
||
def hamiltonian_of_half_bhz_model_for_spin_down(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01):
|
||
hamiltonian = np.zeros((2, 2), dtype=complex)
|
||
varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky))
|
||
d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky))
|
||
d1_d2 = A*(math.sin(kx)+1j*math.sin(ky))
|
||
hamiltonian[0, 0] = varepsilon+d3
|
||
hamiltonian[1, 1] = varepsilon-d3
|
||
hamiltonian[0, 1] = -d1_d2
|
||
hamiltonian[1, 0] = -np.conj(d1_d2)
|
||
return hamiltonian
|
||
|
||
# BBH模型的哈密顿量
|
||
def hamiltonian_of_bbh_model(kx, ky, gamma_x=0.5, gamma_y=0.5, lambda_x=1, lambda_y=1):
|
||
# label of atoms in a unit cell
|
||
# (2) —— (0)
|
||
# | |
|
||
# (1) —— (3)
|
||
hamiltonian = np.zeros((4, 4), dtype=complex)
|
||
hamiltonian[0, 2] = gamma_x+lambda_x*cmath.exp(1j*kx)
|
||
hamiltonian[1, 3] = gamma_x+lambda_x*cmath.exp(-1j*kx)
|
||
hamiltonian[0, 3] = gamma_y+lambda_y*cmath.exp(1j*ky)
|
||
hamiltonian[1, 2] = -gamma_y-lambda_y*cmath.exp(-1j*ky)
|
||
hamiltonian[2, 0] = np.conj(hamiltonian[0, 2])
|
||
hamiltonian[3, 1] = np.conj(hamiltonian[1, 3])
|
||
hamiltonian[3, 0] = np.conj(hamiltonian[0, 3])
|
||
hamiltonian[2, 1] = np.conj(hamiltonian[1, 2])
|
||
return hamiltonian
|
||
|
||
# Kagome模型的哈密顿量
|
||
def hamiltonian_of_kagome_lattice(kx, ky, t=1):
|
||
k1_dot_a1 = kx
|
||
k2_dot_a2 = kx/2+ky*math.sqrt(3)/2
|
||
k3_dot_a3 = -kx/2+ky*math.sqrt(3)/2
|
||
hamiltonian = np.zeros((3, 3), dtype=complex)
|
||
hamiltonian[0, 1] = 2*math.cos(k1_dot_a1)
|
||
hamiltonian[0, 2] = 2*math.cos(k2_dot_a2)
|
||
hamiltonian[1, 2] = 2*math.cos(k3_dot_a3)
|
||
hamiltonian = hamiltonian + hamiltonian.transpose().conj()
|
||
hamiltonian = -t*hamiltonian
|
||
return hamiltonian
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 5: band structures and wave functions
|
||
|
||
## band structures
|
||
|
||
# 计算哈密顿量的本征值
|
||
def calculate_eigenvalue(hamiltonian):
|
||
if np.array(hamiltonian).shape==():
|
||
eigenvalue = np.real(hamiltonian)
|
||
else:
|
||
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
|
||
return eigenvalue
|
||
|
||
# 输入哈密顿量函数（带一组参数），计算一组参数下的本征值，返回本征值向量组
|
||
def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0):
|
||
dim_x = np.array(x_array).shape[0]
|
||
i0 = 0
|
||
if np.array(hamiltonian_function(0)).shape==():
|
||
eigenvalue_array = np.zeros((dim_x, 1))
|
||
for x0 in x_array:
|
||
hamiltonian = hamiltonian_function(x0)
|
||
eigenvalue_array[i0, 0] = np.real(hamiltonian)
|
||
i0 += 1
|
||
else:
|
||
dim = np.array(hamiltonian_function(0)).shape[0]
|
||
eigenvalue_array = np.zeros((dim_x, dim))
|
||
for x0 in x_array:
|
||
if print_show==1:
|
||
print(x0)
|
||
hamiltonian = hamiltonian_function(x0)
|
||
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
|
||
eigenvalue_array[i0, :] = eigenvalue
|
||
i0 += 1
|
||
return eigenvalue_array
|
||
|
||
# 输入哈密顿量函数（带两组参数），计算两组参数下的本征值，返回本征值向量组
|
||
def calculate_eigenvalue_with_two_parameters(x_array, y_array, hamiltonian_function, print_show=0, print_show_more=0):
|
||
dim_x = np.array(x_array).shape[0]
|
||
dim_y = np.array(y_array).shape[0]
|
||
if np.array(hamiltonian_function(0,0)).shape==():
|
||
eigenvalue_array = np.zeros((dim_y, dim_x, 1))
|
||
i0 = 0
|
||
for y0 in y_array:
|
||
j0 = 0
|
||
for x0 in x_array:
|
||
hamiltonian = hamiltonian_function(x0, y0)
|
||
eigenvalue_array[i0, j0, 0] = np.real(hamiltonian)
|
||
j0 += 1
|
||
i0 += 1
|
||
else:
|
||
dim = np.array(hamiltonian_function(0, 0)).shape[0]
|
||
eigenvalue_array = np.zeros((dim_y, dim_x, dim))
|
||
i0 = 0
|
||
for y0 in y_array:
|
||
j0 = 0
|
||
if print_show==1:
|
||
print(y0)
|
||
for x0 in x_array:
|
||
if print_show_more==1:
|
||
print(x0)
|
||
hamiltonian = hamiltonian_function(x0, y0)
|
||
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
|
||
eigenvalue_array[i0, j0, :] = eigenvalue
|
||
j0 += 1
|
||
i0 += 1
|
||
return eigenvalue_array
|
||
|
||
## wave functions
|
||
|
||
# 计算哈密顿量的本征矢
|
||
def calculate_eigenvector(hamiltonian):
|
||
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
|
||
return eigenvector
|
||
|
||
## find vector with the same gauge
|
||
|
||
# 通过二分查找的方法获取和相邻波函数一样规范的波函数
|
||
def find_vector_with_the_same_gauge_with_binary_search(vector_target, vector_ref, show_error=1, show_times=0, show_phase=0, n_test=1000, precision=1e-6):
|
||
phase_1_pre = 0
|
||
phase_2_pre = np.pi
|
||
for i0 in range(n_test):
|
||
test_1 = np.sum(np.abs(vector_target*cmath.exp(1j*phase_1_pre) - vector_ref))
|
||
test_2 = np.sum(np.abs(vector_target*cmath.exp(1j*phase_2_pre) - vector_ref))
|
||
if test_1 < precision:
|
||
phase = phase_1_pre
|
||
if show_times==1:
|
||
print('Binary search times=', i0)
|
||
break
|
||
if i0 == n_test-1:
|
||
phase = phase_1_pre
|
||
if show_error==1:
|
||
print('Gauge not found with binary search times=', i0)
|
||
if test_1 < test_2:
|
||
if i0 == 0:
|
||
phase_1 = phase_1_pre-(phase_2_pre-phase_1_pre)/2
|
||
phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2
|
||
else:
|
||
phase_1 = phase_1_pre
|
||
phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2
|
||
else:
|
||
if i0 == 0:
|
||
phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2
|
||
phase_2 = phase_2_pre+(phase_2_pre-phase_1_pre)/2
|
||
else:
|
||
phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2
|
||
phase_2 = phase_2_pre
|
||
phase_1_pre = phase_1
|
||
phase_2_pre = phase_2
|
||
vector_target = vector_target*cmath.exp(1j*phase)
|
||
if show_phase==1:
|
||
print('Phase=', phase)
|
||
return vector_target
|
||
|
||
# 通过使得波函数的一个非零分量为实数，得到固定规范的波函数
|
||
def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005, index=None):
|
||
vector = np.array(vector)
|
||
if index == None:
|
||
index = np.argmax(np.abs(vector))
|
||
sign_pre = np.sign(np.imag(vector[index]))
|
||
for phase in np.arange(0, 2*np.pi, precision):
|
||
sign = np.sign(np.imag(vector[index]*cmath.exp(1j*phase)))
|
||
if np.abs(np.imag(vector[index]*cmath.exp(1j*phase))) < 1e-9 or sign == -sign_pre:
|
||
break
|
||
sign_pre = sign
|
||
vector = vector*cmath.exp(1j*phase)
|
||
if np.real(vector[index]) < 0:
|
||
vector = -vector
|
||
return vector
|
||
|
||
# 通过使得波函数的一个非零分量为实数，得到固定规范的波函数（在一组波函数中选取最大的那个分量）
|
||
def find_vector_array_with_fixed_gauge_by_making_one_component_real(vector_array, precision=0.005):
|
||
vector_sum = 0
|
||
Num_k = np.array(vector_array).shape[0]
|
||
for i0 in range(Num_k):
|
||
vector_sum += np.abs(vector_array[i0])
|
||
index = np.argmax(np.abs(vector_sum))
|
||
for i0 in range(Num_k):
|
||
vector_array[i0] = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector_array[i0], precision=precision, index=index)
|
||
return vector_array
|
||
|
||
# 旋转两个简并的波函数（说明：参数比较多，效率不高）
|
||
def rotation_of_degenerate_vectors(vector1, vector2, index1=None, index2=None, precision=0.01, criterion=0.01, show_theta=0):
|
||
vector1 = np.array(vector1)
|
||
vector2 = np.array(vector2)
|
||
if index1 == None:
|
||
index1 = np.argmax(np.abs(vector1))
|
||
if index2 == None:
|
||
index2 = np.argmax(np.abs(vector2))
|
||
if np.abs(vector1[index2])>criterion or np.abs(vector2[index1])>criterion:
|
||
for theta in np.arange(0, 2*math.pi, precision):
|
||
if show_theta==1:
|
||
print(theta)
|
||
for phi1 in np.arange(0, 2*math.pi, precision):
|
||
for phi2 in np.arange(0, 2*math.pi, precision):
|
||
vector1_test = cmath.exp(1j*phi1)*vector1*math.cos(theta)+cmath.exp(1j*phi2)*vector2*math.sin(theta)
|
||
vector2_test = -cmath.exp(-1j*phi2)*vector1*math.sin(theta)+cmath.exp(-1j*phi1)*vector2*math.cos(theta)
|
||
if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
|
||
vector1 = vector1_test
|
||
vector2 = vector2_test
|
||
break
|
||
if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
|
||
break
|
||
if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
|
||
break
|
||
return vector1, vector2
|
||
|
||
# 旋转两个简并的波函数向量组（说明：参数比较多，效率不高）
|
||
def rotation_of_degenerate_vectors_array(vector1_array, vector2_array, precision=0.01, criterion=0.01, show_theta=0):
|
||
Num_k = np.array(vector1_array).shape[0]
|
||
vector1_sum = 0
|
||
for i0 in range(Num_k):
|
||
vector1_sum += np.abs(vector1_array[i0])
|
||
index1 = np.argmax(np.abs(vector1_sum))
|
||
vector2_sum = 0
|
||
for i0 in range(Num_k):
|
||
vector2_sum += np.abs(vector2_array[i0])
|
||
index2 = np.argmax(np.abs(vector2_sum))
|
||
for i0 in range(Num_k):
|
||
vector1_array[i0], vector2_array[i0] = guan.rotation_of_degenerate_vectors(vector1=vector1_array[i0], vector2=vector2_array[i0], index1=index1, index2=index2, precision=precision, criterion=criterion, show_theta=show_theta)
|
||
return vector1_array, vector2_array
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 6: Green functions
|
||
|
||
# 输入哈密顿量，得到格林函数
|
||
def green_function(fermi_energy, hamiltonian, broadening, self_energy=0):
|
||
if np.array(hamiltonian).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(hamiltonian).shape[0]
|
||
green = np.linalg.inv((fermi_energy+broadening*1j)*np.eye(dim)-hamiltonian-self_energy)
|
||
return green
|
||
|
||
# 在Dyson方程中的一个中间格林函数G_{nn}^{n}
|
||
def green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening, self_energy=0):
|
||
h01 = np.array(h01)
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
green_nn_n = np.linalg.inv((fermi_energy+broadening*1j)*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), green_nn_n_minus), h01)-self_energy)
|
||
return green_nn_n
|
||
|
||
# 在Dyson方程中的一个中间格林函数G_{in}^{n}
|
||
def green_function_in_n(green_in_n_minus, h01, green_nn_n):
|
||
green_in_n = np.dot(np.dot(green_in_n_minus, h01), green_nn_n)
|
||
return green_in_n
|
||
|
||
# 在Dyson方程中的一个中间格林函数G_{ni}^{n}
|
||
def green_function_ni_n(green_nn_n, h01, green_ni_n_minus):
|
||
h01 = np.array(h01)
|
||
green_ni_n = np.dot(np.dot(green_nn_n, h01.transpose().conj()), green_ni_n_minus)
|
||
return green_ni_n
|
||
|
||
# 在Dyson方程中的一个中间格林函数G_{ii}^{n}
|
||
def green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus):
|
||
green_ii_n = green_ii_n_minus+np.dot(np.dot(np.dot(np.dot(green_in_n_minus, h01), green_nn_n), h01.transpose().conj()),green_ni_n_minus)
|
||
return green_ii_n
|
||
|
||
# 计算转移矩阵（该矩阵可以用来计算表面格林函数）
|
||
def transfer_matrix(fermi_energy, h00, h01):
|
||
h01 = np.array(h01)
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
transfer = np.zeros((2*dim, 2*dim), dtype=complex)
|
||
transfer[0:dim, 0:dim] = np.dot(np.linalg.inv(h01), fermi_energy*np.identity(dim)-h00)
|
||
transfer[0:dim, dim:2*dim] = np.dot(-1*np.linalg.inv(h01), h01.transpose().conj())
|
||
transfer[dim:2*dim, 0:dim] = np.identity(dim)
|
||
transfer[dim:2*dim, dim:2*dim] = 0
|
||
return transfer
|
||
|
||
# 计算电极的表面格林函数
|
||
def surface_green_function_of_lead(fermi_energy, h00, h01):
|
||
h01 = np.array(h01)
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
fermi_energy = fermi_energy+1e-9*1j
|
||
transfer = transfer_matrix(fermi_energy, h00, h01)
|
||
eigenvalue, eigenvector = np.linalg.eig(transfer)
|
||
ind = np.argsort(np.abs(eigenvalue))
|
||
temp = np.zeros((2*dim, 2*dim), dtype=complex)
|
||
i0 = 0
|
||
for ind0 in ind:
|
||
temp[:, i0] = eigenvector[:, ind0]
|
||
i0 += 1
|
||
s1 = temp[dim:2*dim, 0:dim]
|
||
s2 = temp[0:dim, 0:dim]
|
||
s3 = temp[dim:2*dim, dim:2*dim]
|
||
s4 = temp[0:dim, dim:2*dim]
|
||
right_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01, s2), np.linalg.inv(s1)))
|
||
left_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), s3), np.linalg.inv(s4)))
|
||
return right_lead_surface, left_lead_surface
|
||
|
||
# 计算电极的自能（基于Dyson方程的小矩阵形式）
|
||
def self_energy_of_lead(fermi_energy, h00, h01):
|
||
h01 = np.array(h01)
|
||
right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01)
|
||
right_self_energy = np.dot(np.dot(h01, right_lead_surface), h01.transpose().conj())
|
||
left_self_energy = np.dot(np.dot(h01.transpose().conj(), left_lead_surface), h01)
|
||
gamma_right = (right_self_energy - right_self_energy.transpose().conj())*1j
|
||
gamma_left = (left_self_energy - left_self_energy.transpose().conj())*1j
|
||
return right_self_energy, left_self_energy, gamma_right, gamma_left
|
||
|
||
# 计算电极的自能（基于中心区整体的大矩阵形式）
|
||
def self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR):
|
||
h_LC = np.array(h_LC)
|
||
h_CR = np.array(h_CR)
|
||
right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01)
|
||
right_self_energy = np.dot(np.dot(h_CR, right_lead_surface), h_CR.transpose().conj())
|
||
left_self_energy = np.dot(np.dot(h_LC.transpose().conj(), left_lead_surface), h_LC)
|
||
gamma_right = (right_self_energy - right_self_energy.transpose().conj())*1j
|
||
gamma_left = (left_self_energy - left_self_energy.transpose().conj())*1j
|
||
return right_self_energy, left_self_energy, gamma_right, gamma_left
|
||
|
||
# 计算电极的自能（基于中心区整体的大矩阵形式，可适用于多端电导的计算）
|
||
def self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00, h01, h_lead_to_center):
|
||
h_lead_to_center = np.array(h_lead_to_center)
|
||
right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01)
|
||
self_energy = np.dot(np.dot(h_lead_to_center.transpose().conj(), right_lead_surface), h_lead_to_center)
|
||
gamma = (self_energy - self_energy.transpose().conj())*1j
|
||
return self_energy, gamma
|
||
|
||
# 计算考虑电极自能后的中心区的格林函数
|
||
def green_function_with_leads(fermi_energy, h00, h01, h_LC, h_CR, center_hamiltonian):
|
||
dim = np.array(center_hamiltonian).shape[0]
|
||
right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR)
|
||
green = np.linalg.inv(fermi_energy*np.identity(dim)-center_hamiltonian-left_self_energy-right_self_energy)
|
||
return green, gamma_right, gamma_left
|
||
|
||
# 计算用于计算局域电流的格林函数G_n
|
||
def electron_correlation_function_green_n_for_local_current(fermi_energy, h00, h01, h_LC, h_CR, center_hamiltonian):
|
||
right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR)
|
||
green = guan.green_function(fermi_energy, center_hamiltonian, broadening=0, self_energy=left_self_energy+right_self_energy)
|
||
G_n = np.imag(np.dot(np.dot(green, gamma_left), green.transpose().conj()))
|
||
return G_n
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 7: density of states
|
||
|
||
# 计算体系的总态密度
|
||
def total_density_of_states(fermi_energy, hamiltonian, broadening=0.01):
|
||
green = guan.green_function(fermi_energy, hamiltonian, broadening)
|
||
total_dos = -np.trace(np.imag(green))/math.pi
|
||
return total_dos
|
||
|
||
# 对于不同费米能，计算体系的总态密度
|
||
def total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.01, print_show=0):
|
||
dim = np.array(fermi_energy_array).shape[0]
|
||
total_dos_array = np.zeros(dim)
|
||
i0 = 0
|
||
for fermi_energy in fermi_energy_array:
|
||
if print_show == 1:
|
||
print(fermi_energy)
|
||
total_dos_array[i0] = total_density_of_states(fermi_energy, hamiltonian, broadening)
|
||
i0 += 1
|
||
return total_dos_array
|
||
|
||
# 计算方格子的局域态密度（其中，哈密顿量的维度为：dim_hamiltonian = N1*N2*internal_degree）
|
||
def local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1, N2, internal_degree=1, broadening=0.01):
|
||
green = guan.green_function(fermi_energy, hamiltonian, broadening)
|
||
local_dos = np.zeros((N2, N1))
|
||
for i1 in range(N1):
|
||
for i2 in range(N2):
|
||
for i in range(internal_degree):
|
||
local_dos[i2, i1] = local_dos[i2, i1]-np.imag(green[i1*N2*internal_degree+i2*internal_degree+i, i1*N2*internal_degree+i2*internal_degree+i])/math.pi
|
||
return local_dos
|
||
|
||
# 计算立方格子的局域态密度（其中，哈密顿量的维度为：dim_hamiltonian = N1*N2*N3*internal_degree）
|
||
def local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1, N2, N3, internal_degree=1, broadening=0.01):
|
||
green = guan.green_function(fermi_energy, hamiltonian, broadening)
|
||
local_dos = np.zeros((N3, N2, N1))
|
||
for i1 in range(N1):
|
||
for i2 in range(N2):
|
||
for i3 in range(N3):
|
||
for i in range(internal_degree):
|
||
local_dos[i3, i2, i1] = local_dos[i3, i2, i1]-np.imag(green[i1*N2*N3*internal_degree+i2*N3*internal_degree+i3*internal_degree+i, i1*N2*N3*internal_degree+i2*N3*internal_degree+i3*internal_degree+i])/math.pi
|
||
return local_dos
|
||
|
||
# 利用Dyson方程，计算方格子的局域态密度（其中，h00的维度为：dim_h00 = N2*internal_degree）
|
||
def local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00, h01, N2, N1, internal_degree=1, broadening=0.01):
|
||
local_dos = np.zeros((N2, N1))
|
||
green_11_1 = guan.green_function(fermi_energy, h00, broadening)
|
||
for i1 in range(N1):
|
||
green_nn_n_minus = green_11_1
|
||
green_in_n_minus = green_11_1
|
||
green_ni_n_minus = green_11_1
|
||
green_ii_n_minus = green_11_1
|
||
for i2_0 in range(i1):
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
||
green_nn_n_minus = green_nn_n
|
||
if i1!=0:
|
||
green_in_n_minus = green_nn_n
|
||
green_ni_n_minus = green_nn_n
|
||
green_ii_n_minus = green_nn_n
|
||
for size_0 in range(N1-1-i1):
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
||
green_nn_n_minus = green_nn_n
|
||
green_ii_n = guan.green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus)
|
||
green_ii_n_minus = green_ii_n
|
||
green_in_n = guan.green_function_in_n(green_in_n_minus, h01, green_nn_n)
|
||
green_in_n_minus = green_in_n
|
||
green_ni_n = guan.green_function_ni_n(green_nn_n, h01, green_ni_n_minus)
|
||
green_ni_n_minus = green_ni_n
|
||
for i2 in range(N2):
|
||
for i in range(internal_degree):
|
||
local_dos[i2, i1] = local_dos[i2, i1] - np.imag(green_ii_n_minus[i2*internal_degree+i, i2*internal_degree+i])/math.pi
|
||
return local_dos
|
||
|
||
# 利用Dyson方程，计算立方格子的局域态密度（其中，h00的维度为：dim_h00 = N2*N3*internal_degree）
|
||
def local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3, N2, N1, internal_degree=1, broadening=0.01):
|
||
local_dos = np.zeros((N3, N2, N1))
|
||
green_11_1 = guan.green_function(fermi_energy, h00, broadening)
|
||
for i1 in range(N1):
|
||
green_nn_n_minus = green_11_1
|
||
green_in_n_minus = green_11_1
|
||
green_ni_n_minus = green_11_1
|
||
green_ii_n_minus = green_11_1
|
||
for i1_0 in range(i1):
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
||
green_nn_n_minus = green_nn_n
|
||
if i1!=0:
|
||
green_in_n_minus = green_nn_n
|
||
green_ni_n_minus = green_nn_n
|
||
green_ii_n_minus = green_nn_n
|
||
for size_0 in range(N1-1-i1):
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
||
green_nn_n_minus = green_nn_n
|
||
green_ii_n = guan.green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus)
|
||
green_ii_n_minus = green_ii_n
|
||
green_in_n = guan.green_function_in_n(green_in_n_minus, h01, green_nn_n)
|
||
green_in_n_minus = green_in_n
|
||
green_ni_n = guan.green_function_ni_n(green_nn_n, h01, green_ni_n_minus)
|
||
green_ni_n_minus = green_ni_n
|
||
for i2 in range(N2):
|
||
for i3 in range(N3):
|
||
for i in range(internal_degree):
|
||
local_dos[i3, i2, i1] = local_dos[i3, i2, i1] -np.imag(green_ii_n_minus[i2*N3*internal_degree+i3*internal_degree+i, i2*N3*internal_degree+i3*internal_degree+i])/math.pi
|
||
return local_dos
|
||
|
||
# 利用Dyson方程，计算方格子条带（考虑了电极自能）的局域态密度（其中，h00的维度为：dim_h00 = N2*internal_degree）
|
||
def local_density_of_states_for_square_lattice_with_self_energy_using_dyson_equation(fermi_energy, h00, h01, N2, N1, right_self_energy, left_self_energy, internal_degree=1, broadening=0.01):
|
||
local_dos = np.zeros((N2, N1))
|
||
green_11_1 = guan.green_function(fermi_energy, h00+left_self_energy, broadening)
|
||
for i1 in range(N1):
|
||
green_nn_n_minus = green_11_1
|
||
green_in_n_minus = green_11_1
|
||
green_ni_n_minus = green_11_1
|
||
green_ii_n_minus = green_11_1
|
||
for i2_0 in range(i1):
|
||
if i2_0 == N1-1-1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+right_self_energy, h01, green_nn_n_minus, broadening)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
||
green_nn_n_minus = green_nn_n
|
||
if i1!=0:
|
||
green_in_n_minus = green_nn_n
|
||
green_ni_n_minus = green_nn_n
|
||
green_ii_n_minus = green_nn_n
|
||
for size_0 in range(N1-1-i1):
|
||
if size_0 == N1-1-i1-1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+right_self_energy, h01, green_nn_n_minus, broadening)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening)
|
||
green_nn_n_minus = green_nn_n
|
||
green_ii_n = guan.green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus)
|
||
green_ii_n_minus = green_ii_n
|
||
green_in_n = guan.green_function_in_n(green_in_n_minus, h01, green_nn_n)
|
||
green_in_n_minus = green_in_n
|
||
green_ni_n = guan.green_function_ni_n(green_nn_n, h01, green_ni_n_minus)
|
||
green_ni_n_minus = green_ni_n
|
||
for i2 in range(N2):
|
||
for i in range(internal_degree):
|
||
local_dos[i2, i1] = local_dos[i2, i1] - np.imag(green_ii_n_minus[i2*internal_degree+i, i2*internal_degree+i])/math.pi
|
||
return local_dos
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 8: quantum transport
|
||
|
||
## conductance
|
||
|
||
# 计算电导
|
||
def calculate_conductance(fermi_energy, h00, h01, length=100):
|
||
import copy
|
||
right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
|
||
for ix in range(length):
|
||
if ix == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
elif ix != length-1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
|
||
return conductance
|
||
|
||
# 计算不同费米能下的电导
|
||
def calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01, length=100, print_show=0):
|
||
dim = np.array(fermi_energy_array).shape[0]
|
||
conductance_array = np.zeros(dim)
|
||
i0 = 0
|
||
for fermi_energy in fermi_energy_array:
|
||
conductance_array[i0] = np.real(guan.calculate_conductance(fermi_energy, h00, h01, length))
|
||
if print_show == 1:
|
||
print(fermi_energy, conductance_array[i0])
|
||
i0 += 1
|
||
return conductance_array
|
||
|
||
# 计算在势垒散射下的电导
|
||
def calculate_conductance_with_barrier(fermi_energy, h00, h01, length=100, barrier_length=20, barrier_potential=1):
|
||
import copy
|
||
right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
|
||
dim = np.array(h00).shape[0]
|
||
for ix in range(length):
|
||
if ix == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
elif int(length/2-barrier_length/2)<=ix<int(length/2+barrier_length/2):
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+barrier_potential*np.identity(dim), h01, green_nn_n, broadening=0)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
elif ix != length-1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
|
||
return conductance
|
||
|
||
# 计算在无序散射下的电导
|
||
def calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100, calculation_times=1):
|
||
import copy
|
||
right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
|
||
dim = np.array(h00).shape[0]
|
||
conductance_averaged = 0
|
||
for times in range(calculation_times):
|
||
for ix in range(length+2):
|
||
disorder = np.zeros((dim, dim))
|
||
for dim0 in range(dim):
|
||
if np.random.uniform(0, 1)<=disorder_concentration:
|
||
disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
|
||
if ix == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
elif ix != length+1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
|
||
conductance_averaged += conductance
|
||
conductance_averaged = conductance_averaged/calculation_times
|
||
return conductance_averaged
|
||
|
||
# 计算在无序垂直切片的散射下的电导
|
||
def calculate_conductance_with_slice_disorder(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100):
|
||
import copy
|
||
right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
|
||
dim = np.array(h00).shape[0]
|
||
for ix in range(length+2):
|
||
disorder = np.zeros((dim, dim))
|
||
if np.random.uniform(0, 1)<=disorder_concentration:
|
||
disorder = np.random.uniform(-disorder_intensity, disorder_intensity)*np.eye(dim)
|
||
if ix == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
elif ix != length+1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
|
||
return conductance
|
||
|
||
# 计算在无序水平切片的散射下的电导
|
||
def calculate_conductance_with_disorder_inside_unit_cell_which_keeps_translational_symmetry(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100):
|
||
import copy
|
||
right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
|
||
dim = np.array(h00).shape[0]
|
||
disorder = np.zeros((dim, dim))
|
||
for dim0 in range(dim):
|
||
if np.random.uniform(0, 1)<=disorder_concentration:
|
||
disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
|
||
for ix in range(length+2):
|
||
if ix == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
elif ix != length+1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
|
||
return conductance
|
||
|
||
# 计算在随机空位的散射下的电导
|
||
def calculate_conductance_with_random_vacancy(fermi_energy, h00, h01, vacancy_concentration=0.5, vacancy_potential=1e9, length=100):
|
||
import copy
|
||
right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
|
||
dim = np.array(h00).shape[0]
|
||
for ix in range(length+2):
|
||
random_vacancy = np.zeros((dim, dim))
|
||
for dim0 in range(dim):
|
||
if np.random.uniform(0, 1)<=vacancy_concentration:
|
||
random_vacancy[dim0, dim0] = vacancy_potential
|
||
if ix == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
elif ix != length+1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+random_vacancy, h01, green_nn_n, broadening=0)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
|
||
return conductance
|
||
|
||
# 计算在不同无序散射强度下的电导
|
||
def calculate_conductance_with_disorder_intensity_array(fermi_energy, h00, h01, disorder_intensity_array, disorder_concentration=1.0, length=100, calculation_times=1, print_show=0):
|
||
dim = np.array(disorder_intensity_array).shape[0]
|
||
conductance_array = np.zeros(dim)
|
||
i0 = 0
|
||
for disorder_intensity in disorder_intensity_array:
|
||
for times in range(calculation_times):
|
||
conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
|
||
if print_show == 1:
|
||
print(disorder_intensity, conductance_array[i0]/calculation_times)
|
||
i0 += 1
|
||
conductance_array = conductance_array/calculation_times
|
||
return conductance_array
|
||
|
||
# 计算在不同无序浓度下的电导
|
||
def calculate_conductance_with_disorder_concentration_array(fermi_energy, h00, h01, disorder_concentration_array, disorder_intensity=2.0, length=100, calculation_times=1, print_show=0):
|
||
dim = np.array(disorder_concentration_array).shape[0]
|
||
conductance_array = np.zeros(dim)
|
||
i0 = 0
|
||
for disorder_concentration in disorder_concentration_array:
|
||
for times in range(calculation_times):
|
||
conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
|
||
if print_show == 1:
|
||
print(disorder_concentration, conductance_array[i0]/calculation_times)
|
||
i0 += 1
|
||
conductance_array = conductance_array/calculation_times
|
||
return conductance_array
|
||
|
||
# 计算在不同无序散射长度下的电导
|
||
def calculate_conductance_with_scattering_length_array(fermi_energy, h00, h01, length_array, disorder_intensity=2.0, disorder_concentration=1.0, calculation_times=1, print_show=0):
|
||
dim = np.array(length_array).shape[0]
|
||
conductance_array = np.zeros(dim)
|
||
i0 = 0
|
||
for length in length_array:
|
||
for times in range(calculation_times):
|
||
conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
|
||
if print_show == 1:
|
||
print(length, conductance_array[i0]/calculation_times)
|
||
i0 += 1
|
||
conductance_array = conductance_array/calculation_times
|
||
return conductance_array
|
||
|
||
## multi-terminal transmission
|
||
|
||
# 计算得到Gamma矩阵和格林函数，用于计算六端口的量子输运
|
||
def get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
|
||
# ---------------- Geometry ----------------
|
||
# lead2 lead3
|
||
# lead1(L) lead4(R)
|
||
# lead6 lead5
|
||
h00_for_lead_1 = h00_for_lead_4
|
||
h00_for_lead_2 = h00_for_lead_2
|
||
h00_for_lead_3 = h00_for_lead_2
|
||
h00_for_lead_5 = h00_for_lead_2
|
||
h00_for_lead_6 = h00_for_lead_2
|
||
h00_for_lead_4 = h00_for_lead_4
|
||
h01_for_lead_1 = h01_for_lead_4.transpose().conj()
|
||
h01_for_lead_2 = h01_for_lead_2
|
||
h01_for_lead_3 = h01_for_lead_2
|
||
h01_for_lead_4 = h01_for_lead_4
|
||
h01_for_lead_5 = h01_for_lead_2.transpose().conj()
|
||
h01_for_lead_6 = h01_for_lead_2.transpose().conj()
|
||
h_lead1_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
|
||
h_lead2_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
|
||
h_lead3_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
|
||
h_lead4_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
|
||
h_lead5_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
|
||
h_lead6_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
|
||
move = moving_step_of_leads # the step of leads 2,3,6,5 moving to center
|
||
h_lead1_to_center[0:internal_degree*width, 0:internal_degree*width] = h01_for_lead_1.transpose().conj()
|
||
h_lead4_to_center[0:internal_degree*width, internal_degree*width*(length-1):internal_degree*width*length] = h01_for_lead_4.transpose().conj()
|
||
for i0 in range(width):
|
||
begin_index = internal_degree*i0+0
|
||
end_index = internal_degree*i0+internal_degree
|
||
h_lead2_to_center[begin_index:end_index, internal_degree*(width*(move+i0)+(width-1))+0:internal_degree*(width*(move+i0)+(width-1))+internal_degree] = h01_for_lead_2.transpose().conj()[begin_index:end_index, begin_index:end_index]
|
||
h_lead3_to_center[begin_index:end_index, internal_degree*(width*(length-move-1-i0)+(width-1))+0:internal_degree*(width*(length-move-1-i0)+(width-1))+internal_degree] = h01_for_lead_3.transpose().conj()[begin_index:end_index, begin_index:end_index]
|
||
h_lead5_to_center[begin_index:end_index, internal_degree*(width*(length-move-1-i0)+0)+0:internal_degree*(width*(length-move-1-i0)+0)+internal_degree] = h01_for_lead_5.transpose().conj()[begin_index:end_index, begin_index:end_index]
|
||
h_lead6_to_center[begin_index:end_index, internal_degree*(width*(i0+move)+0)+0:internal_degree*(width*(i0+move)+0)+internal_degree] = h01_for_lead_6.transpose().conj()[begin_index:end_index, begin_index:end_index]
|
||
self_energy1, gamma1 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_1, h01_for_lead_1, h_lead1_to_center)
|
||
self_energy2, gamma2 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_2, h01_for_lead_1, h_lead2_to_center)
|
||
self_energy3, gamma3 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_3, h01_for_lead_1, h_lead3_to_center)
|
||
self_energy4, gamma4 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_4, h01_for_lead_1, h_lead4_to_center)
|
||
self_energy5, gamma5 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_5, h01_for_lead_1, h_lead5_to_center)
|
||
self_energy6, gamma6 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_6, h01_for_lead_1, h_lead6_to_center)
|
||
gamma_array = [gamma1, gamma2, gamma3, gamma4, gamma5, gamma6]
|
||
green = np.linalg.inv(fermi_energy*np.eye(internal_degree*width*length)-center_hamiltonian-self_energy1-self_energy2-self_energy3-self_energy4-self_energy5-self_energy6)
|
||
return gamma_array, green
|
||
|
||
# 计算六端口的透射矩阵
|
||
def calculate_six_terminal_transmission_matrix(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
|
||
gamma_array, green = guan.get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width, length, internal_degree, moving_step_of_leads)
|
||
transmission_matrix = np.zeros((6, 6), dtype=complex)
|
||
channel_lead_4 = guan.calculate_conductance(fermi_energy, h00_for_lead_4, h01_for_lead_4, length=3)
|
||
channel_lead_2 = guan.calculate_conductance(fermi_energy, h00_for_lead_2, h01_for_lead_2, length=3)
|
||
for i0 in range(6):
|
||
for j0 in range(6):
|
||
if j0!=i0:
|
||
transmission_matrix[i0, j0] = np.trace(np.dot(np.dot(np.dot(gamma_array[i0], green), gamma_array[j0]), green.transpose().conj()))
|
||
for i0 in range(6):
|
||
if i0 == 0 or i0 == 3:
|
||
transmission_matrix[i0, i0] = channel_lead_4
|
||
else:
|
||
transmission_matrix[i0, i0] = channel_lead_2
|
||
for i0 in range(6):
|
||
for j0 in range(6):
|
||
if j0!=i0:
|
||
transmission_matrix[i0, i0] = transmission_matrix[i0, i0]-transmission_matrix[i0, j0]
|
||
transmission_matrix = np.real(transmission_matrix)
|
||
return transmission_matrix
|
||
|
||
# 计算从电极1出发的透射系数
|
||
def calculate_six_terminal_transmissions_from_lead_1(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
|
||
gamma_array, green = guan.get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width, length, internal_degree, moving_step_of_leads)
|
||
transmission_12 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[1]), green.transpose().conj())))
|
||
transmission_13 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[2]), green.transpose().conj())))
|
||
transmission_14 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[3]), green.transpose().conj())))
|
||
transmission_15 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[4]), green.transpose().conj())))
|
||
transmission_16 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[5]), green.transpose().conj())))
|
||
return transmission_12, transmission_13, transmission_14, transmission_15, transmission_16
|
||
|
||
## scattering matrix
|
||
|
||
# 通过动量k的虚部，判断通道为传播通道还是衰减通道
|
||
def if_active_channel(k_of_channel):
|
||
if np.abs(np.imag(k_of_channel))<1e-6:
|
||
if_active = 1
|
||
else:
|
||
if_active = 0
|
||
return if_active
|
||
|
||
# 获取通道的动量和速度，用于计算散射矩阵
|
||
def get_k_and_velocity_of_channel(fermi_energy, h00, h01):
|
||
import copy
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
transfer = guan.transfer_matrix(fermi_energy, h00, h01)
|
||
eigenvalue, eigenvector = np.linalg.eig(transfer)
|
||
k_of_channel = np.log(eigenvalue)/1j
|
||
ind = np.argsort(np.real(k_of_channel))
|
||
k_of_channel = np.sort(k_of_channel)
|
||
temp = np.zeros((2*dim, 2*dim), dtype=complex)
|
||
temp2 = np.zeros((2*dim), dtype=complex)
|
||
i0 = 0
|
||
for ind0 in ind:
|
||
temp[:, i0] = eigenvector[:, ind0]
|
||
temp2[i0] = eigenvalue[ind0]
|
||
i0 += 1
|
||
eigenvalue = copy.deepcopy(temp2)
|
||
temp = temp[0:dim, :]
|
||
factor = np.zeros(2*dim)
|
||
for dim0 in range(dim):
|
||
factor = factor+np.square(np.abs(temp[dim0, :]))
|
||
for dim0 in range(2*dim):
|
||
temp[:, dim0] = temp[:, dim0]/math.sqrt(factor[dim0])
|
||
velocity_of_channel = np.zeros((2*dim), dtype=complex)
|
||
for dim0 in range(2*dim):
|
||
velocity_of_channel[dim0] = eigenvalue[dim0]*np.dot(np.dot(temp[0:dim, :].transpose().conj(), h01),temp[0:dim, :])[dim0, dim0]
|
||
velocity_of_channel = -2*np.imag(velocity_of_channel)
|
||
eigenvector = copy.deepcopy(temp)
|
||
return k_of_channel, velocity_of_channel, eigenvalue, eigenvector
|
||
|
||
# 获取分类后的动量和速度，以及U和F，用于计算散射矩阵
|
||
def get_classified_k_velocity_u_and_f(fermi_energy, h00, h01):
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
k_of_channel, velocity_of_channel, eigenvalue, eigenvector = guan.get_k_and_velocity_of_channel(fermi_energy, h00, h01)
|
||
ind_right_active = 0; ind_right_evanescent = 0; ind_left_active = 0; ind_left_evanescent = 0
|
||
k_right = np.zeros(dim, dtype=complex); k_left = np.zeros(dim, dtype=complex)
|
||
velocity_right = np.zeros(dim, dtype=complex); velocity_left = np.zeros(dim, dtype=complex)
|
||
lambda_right = np.zeros(dim, dtype=complex); lambda_left = np.zeros(dim, dtype=complex)
|
||
u_right = np.zeros((dim, dim), dtype=complex); u_left = np.zeros((dim, dim), dtype=complex)
|
||
for dim0 in range(2*dim):
|
||
if_active = guan.if_active_channel(k_of_channel[dim0])
|
||
if guan.if_active_channel(k_of_channel[dim0]) == 1:
|
||
direction = np.sign(velocity_of_channel[dim0])
|
||
else:
|
||
direction = np.sign(np.imag(k_of_channel[dim0]))
|
||
if direction == 1:
|
||
if if_active == 1: # right-moving active channel
|
||
k_right[ind_right_active] = k_of_channel[dim0]
|
||
velocity_right[ind_right_active] = velocity_of_channel[dim0]
|
||
lambda_right[ind_right_active] = eigenvalue[dim0]
|
||
u_right[:, ind_right_active] = eigenvector[:, dim0]
|
||
ind_right_active += 1
|
||
else: # right-moving evanescent channel
|
||
k_right[dim-1-ind_right_evanescent] = k_of_channel[dim0]
|
||
velocity_right[dim-1-ind_right_evanescent] = velocity_of_channel[dim0]
|
||
lambda_right[dim-1-ind_right_evanescent] = eigenvalue[dim0]
|
||
u_right[:, dim-1-ind_right_evanescent] = eigenvector[:, dim0]
|
||
ind_right_evanescent += 1
|
||
else:
|
||
if if_active == 1: # left-moving active channel
|
||
k_left[ind_left_active] = k_of_channel[dim0]
|
||
velocity_left[ind_left_active] = velocity_of_channel[dim0]
|
||
lambda_left[ind_left_active] = eigenvalue[dim0]
|
||
u_left[:, ind_left_active] = eigenvector[:, dim0]
|
||
ind_left_active += 1
|
||
else: # left-moving evanescent channel
|
||
k_left[dim-1-ind_left_evanescent] = k_of_channel[dim0]
|
||
velocity_left[dim-1-ind_left_evanescent] = velocity_of_channel[dim0]
|
||
lambda_left[dim-1-ind_left_evanescent] = eigenvalue[dim0]
|
||
u_left[:, dim-1-ind_left_evanescent] = eigenvector[:, dim0]
|
||
ind_left_evanescent += 1
|
||
lambda_matrix_right = np.diag(lambda_right)
|
||
lambda_matrix_left = np.diag(lambda_left)
|
||
f_right = np.dot(np.dot(u_right, lambda_matrix_right), np.linalg.inv(u_right))
|
||
f_left = np.dot(np.dot(u_left, lambda_matrix_left), np.linalg.inv(u_left))
|
||
return k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active
|
||
|
||
# 计算散射矩阵
|
||
def calculate_scattering_matrix(fermi_energy, h00, h01, length=100):
|
||
import copy
|
||
h01 = np.array(h01)
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active = guan.get_classified_k_velocity_u_and_f(fermi_energy, h00, h01)
|
||
right_self_energy = np.dot(h01, f_right)
|
||
left_self_energy = np.dot(h01.transpose().conj(), np.linalg.inv(f_left))
|
||
for i0 in range(length):
|
||
if i0 == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_00_n = copy.deepcopy(green_nn_n)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
green_n0_n = copy.deepcopy(green_nn_n)
|
||
elif i0 != length-1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_00_n = guan.green_function_ii_n(green_00_n, green_0n_n, h01, green_nn_n, green_n0_n)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
green_n0_n = guan.green_function_ni_n(green_nn_n, h01, green_n0_n)
|
||
temp = np.dot(h01.transpose().conj(), np.linalg.inv(f_right)-np.linalg.inv(f_left))
|
||
transmission_matrix = np.dot(np.dot(np.linalg.inv(u_right), np.dot(green_n0_n, temp)), u_right)
|
||
reflection_matrix = np.dot(np.dot(np.linalg.inv(u_left), np.dot(green_00_n, temp)-np.identity(dim)), u_right)
|
||
for dim0 in range(dim):
|
||
for dim1 in range(dim):
|
||
if_active = guan.if_active_channel(k_right[dim0])*guan.if_active_channel(k_right[dim1])
|
||
if if_active == 1:
|
||
transmission_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_right[dim0]/velocity_right[dim1])) * transmission_matrix[dim0, dim1]
|
||
reflection_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_left[dim0]/velocity_right[dim1]))*reflection_matrix[dim0, dim1]
|
||
else:
|
||
transmission_matrix[dim0, dim1] = 0
|
||
reflection_matrix[dim0, dim1] = 0
|
||
sum_of_tran_refl_array = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)+np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
for sum_of_tran_refl in sum_of_tran_refl_array:
|
||
if sum_of_tran_refl > 1.001:
|
||
print('Error Alert: scattering matrix is not normalized!')
|
||
return transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active
|
||
|
||
# 从散射矩阵中，获取散射矩阵的信息
|
||
def information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active):
|
||
if np.array(transmission_matrix).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(transmission_matrix).shape[0]
|
||
number_of_active_channels = ind_right_active
|
||
number_of_evanescent_channels = dim-ind_right_active
|
||
k_of_right_moving_active_channels = np.real(k_right[0:ind_right_active])
|
||
k_of_left_moving_active_channels = np.real(k_left[0:ind_right_active])
|
||
velocity_of_right_moving_active_channels = np.real(velocity_right[0:ind_right_active])
|
||
velocity_of_left_moving_active_channels = np.real(velocity_left[0:ind_right_active])
|
||
transmission_matrix_for_active_channels = np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active]))
|
||
reflection_matrix_for_active_channels = np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active]))
|
||
total_transmission_of_channels = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
total_conductance = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])))
|
||
total_reflection_of_channels = np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
sum_of_transmission_and_reflection_of_channels = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0) + np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
return number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels
|
||
|
||
# 已知h00和h01，计算散射矩阵并获得散射矩阵的信息
|
||
def calculate_scattering_matrix_and_get_information(fermi_energy, h00, h01, length=100):
|
||
transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix(fermi_energy, h00, h01, length=length)
|
||
|
||
number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)
|
||
|
||
return number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels
|
||
|
||
# 从散射矩阵中，打印出散射矩阵的信息
|
||
def print_or_write_scattering_matrix_with_information_of_scattering_matrix(number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels, print_show=1, write_file=0, filename='a', file_format='.txt'):
|
||
if print_show == 1:
|
||
print('\nActive channel (left or right) = ', number_of_active_channels)
|
||
print('Evanescent channel (left or right) = ', number_of_evanescent_channels, '\n')
|
||
print('K of right-moving active channels:\n', k_of_right_moving_active_channels)
|
||
print('K of left-moving active channels:\n', k_of_left_moving_active_channels, '\n')
|
||
print('Velocity of right-moving active channels:\n', velocity_of_right_moving_active_channels)
|
||
print('Velocity of left-moving active channels:\n', velocity_of_left_moving_active_channels, '\n')
|
||
print('Transmission matrix:\n', transmission_matrix_for_active_channels)
|
||
print('Reflection matrix:\n', reflection_matrix_for_active_channels, '\n')
|
||
print('Total transmission of channels:\n', total_transmission_of_channels)
|
||
print('Total conductance = ', total_conductance, '\n')
|
||
print('Total reflection of channels:\n', total_reflection_of_channels)
|
||
print('Sum of transmission and reflection of channels:\n', sum_of_transmission_and_reflection_of_channels, '\n')
|
||
if write_file == 1:
|
||
with open(filename+file_format, 'w') as f:
|
||
f.write('Active channel (left or right) = ' + str(number_of_active_channels) + '\n')
|
||
f.write('Evanescent channel (left or right) = ' + str(number_of_evanescent_channels) + '\n\n')
|
||
f.write('Channel K Velocity\n')
|
||
for ind0 in range(number_of_active_channels):
|
||
f.write(' '+str(ind0 + 1) + ' | '+str(k_of_right_moving_active_channels[ind0])+' ' + str(velocity_of_right_moving_active_channels[ind0])+'\n')
|
||
f.write('\n')
|
||
for ind0 in range(number_of_active_channels):
|
||
f.write(' -' + str(ind0 + 1) + ' | ' + str(k_of_left_moving_active_channels[ind0]) + ' ' + str(velocity_of_left_moving_active_channels[ind0]) + '\n')
|
||
f.write('\nScattering matrix:\n ')
|
||
for ind0 in range(number_of_active_channels):
|
||
f.write(str(ind0+1)+' ')
|
||
f.write('\n')
|
||
for ind1 in range(number_of_active_channels):
|
||
f.write(' '+str(ind1+1)+' ')
|
||
for ind2 in range(number_of_active_channels):
|
||
f.write('%f' % transmission_matrix_for_active_channels[ind1, ind2]+' ')
|
||
f.write('\n')
|
||
f.write('\n')
|
||
for ind1 in range(number_of_active_channels):
|
||
f.write(' -'+str(ind1+1)+' ')
|
||
for ind2 in range(number_of_active_channels):
|
||
f.write('%f' % reflection_matrix_for_active_channels[ind1, ind2]+' ')
|
||
f.write('\n')
|
||
f.write('\n')
|
||
f.write('Total transmission of channels:\n'+str(total_transmission_of_channels)+'\n')
|
||
f.write('Total conductance = '+str(total_conductance)+'\n')
|
||
|
||
# 已知h00和h01，计算散射矩阵并打印出散射矩阵的信息
|
||
def print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, print_show=1, write_file=0, filename='a', file_format='.txt'):
|
||
transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix(fermi_energy, h00, h01, length=length)
|
||
|
||
number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)
|
||
|
||
guan.print_or_write_scattering_matrix_with_information_of_scattering_matrix(number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels, print_show=print_show, write_file=write_file, filename=filename, file_format=file_format)
|
||
|
||
# 在无序下，计算散射矩阵
|
||
def calculate_scattering_matrix_with_disorder(fermi_energy, h00, h01, length=100, disorder_intensity=2.0, disorder_concentration=1.0):
|
||
import copy
|
||
h01 = np.array(h01)
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active = guan.get_classified_k_velocity_u_and_f(fermi_energy, h00, h01)
|
||
right_self_energy = np.dot(h01, f_right)
|
||
left_self_energy = np.dot(h01.transpose().conj(), np.linalg.inv(f_left))
|
||
for i0 in range(length):
|
||
disorder = np.zeros((dim, dim))
|
||
for dim0 in range(dim):
|
||
if np.random.uniform(0, 1)<=disorder_concentration:
|
||
disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
|
||
if i0 == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_00_n = copy.deepcopy(green_nn_n)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
green_n0_n = copy.deepcopy(green_nn_n)
|
||
elif i0 != length-1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_00_n = guan.green_function_ii_n(green_00_n, green_0n_n, h01, green_nn_n, green_n0_n)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
green_n0_n = guan.green_function_ni_n(green_nn_n, h01, green_n0_n)
|
||
temp = np.dot(h01.transpose().conj(), np.linalg.inv(f_right)-np.linalg.inv(f_left))
|
||
transmission_matrix = np.dot(np.dot(np.linalg.inv(u_right), np.dot(green_n0_n, temp)), u_right)
|
||
reflection_matrix = np.dot(np.dot(np.linalg.inv(u_left), np.dot(green_00_n, temp)-np.identity(dim)), u_right)
|
||
for dim0 in range(dim):
|
||
for dim1 in range(dim):
|
||
if_active = guan.if_active_channel(k_right[dim0])*guan.if_active_channel(k_right[dim1])
|
||
if if_active == 1:
|
||
transmission_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_right[dim0]/velocity_right[dim1])) * transmission_matrix[dim0, dim1]
|
||
reflection_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_left[dim0]/velocity_right[dim1]))*reflection_matrix[dim0, dim1]
|
||
else:
|
||
transmission_matrix[dim0, dim1] = 0
|
||
reflection_matrix[dim0, dim1] = 0
|
||
sum_of_tran_refl_array = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)+np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
for sum_of_tran_refl in sum_of_tran_refl_array:
|
||
if sum_of_tran_refl > 1.001:
|
||
print('Error Alert: scattering matrix is not normalized!')
|
||
return transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active
|
||
|
||
# 在无序下，计算散射矩阵，并获取散射矩阵多次计算的平均信息
|
||
def calculate_scattering_matrix_with_disorder_and_get_averaged_information(fermi_energy, h00, h01, length=100, disorder_intensity=2.0, disorder_concentration=1.0, calculation_times=1):
|
||
transmission_matrix_for_active_channels_averaged = 0
|
||
reflection_matrix_for_active_channels_averaged = 0
|
||
for i0 in range(calculation_times):
|
||
transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix_with_disorder(fermi_energy, h00, h01, length, disorder_intensity, disorder_concentration)
|
||
|
||
number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)
|
||
|
||
transmission_matrix_for_active_channels_averaged += transmission_matrix_for_active_channels
|
||
reflection_matrix_for_active_channels_averaged += reflection_matrix_for_active_channels
|
||
transmission_matrix_for_active_channels_averaged = transmission_matrix_for_active_channels_averaged/calculation_times
|
||
reflection_matrix_for_active_channels_averaged = reflection_matrix_for_active_channels_averaged/calculation_times
|
||
return transmission_matrix_for_active_channels_averaged, reflection_matrix_for_active_channels_averaged
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 9: topological invariant
|
||
|
||
# 通过高效法计算方格子的陈数
|
||
def calculate_chern_number_for_square_lattice_with_efficient_method(hamiltonian_function, precision=100, print_show=0):
|
||
if np.array(hamiltonian_function(0, 0)).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(hamiltonian_function(0, 0)).shape[0]
|
||
delta = 2*math.pi/precision
|
||
chern_number = np.zeros(dim, dtype=complex)
|
||
for kx in np.arange(-math.pi, math.pi, delta):
|
||
if print_show == 1:
|
||
print(kx)
|
||
for ky in np.arange(-math.pi, math.pi, delta):
|
||
H = hamiltonian_function(kx, ky)
|
||
vector = guan.calculate_eigenvector(H)
|
||
H_delta_kx = hamiltonian_function(kx+delta, ky)
|
||
vector_delta_kx = guan.calculate_eigenvector(H_delta_kx)
|
||
H_delta_ky = hamiltonian_function(kx, ky+delta)
|
||
vector_delta_ky = guan.calculate_eigenvector(H_delta_ky)
|
||
H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
|
||
vector_delta_kx_ky = guan.calculate_eigenvector(H_delta_kx_ky)
|
||
for i in range(dim):
|
||
vector_i = vector[:, i]
|
||
vector_delta_kx_i = vector_delta_kx[:, i]
|
||
vector_delta_ky_i = vector_delta_ky[:, i]
|
||
vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
|
||
Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
|
||
Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
|
||
Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
|
||
Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
|
||
F = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))
|
||
chern_number[i] = chern_number[i] + F
|
||
chern_number = chern_number/(2*math.pi*1j)
|
||
return chern_number
|
||
|
||
# 通过高效法计算方格子的陈数（可计算简并的情况）
|
||
def calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision=100, print_show=0):
|
||
delta = 2*math.pi/precision
|
||
chern_number = 0
|
||
for kx in np.arange(-math.pi, math.pi, delta):
|
||
if print_show == 1:
|
||
print(kx)
|
||
for ky in np.arange(-math.pi, math.pi, delta):
|
||
H = hamiltonian_function(kx, ky)
|
||
eigenvalue, vector = np.linalg.eigh(H)
|
||
H_delta_kx = hamiltonian_function(kx+delta, ky)
|
||
eigenvalue, vector_delta_kx = np.linalg.eigh(H_delta_kx)
|
||
H_delta_ky = hamiltonian_function(kx, ky+delta)
|
||
eigenvalue, vector_delta_ky = np.linalg.eigh(H_delta_ky)
|
||
H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
|
||
eigenvalue, vector_delta_kx_ky = np.linalg.eigh(H_delta_kx_ky)
|
||
dim = len(index_of_bands)
|
||
det_value = 1
|
||
# first dot product
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i0 = 0
|
||
for dim1 in index_of_bands:
|
||
j0 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i0, j0] = np.dot(np.conj(vector[:, dim1]), vector_delta_kx[:, dim2])
|
||
j0 += 1
|
||
i0 += 1
|
||
dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
|
||
det_value = det_value*dot_matrix
|
||
# second dot product
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i0 = 0
|
||
for dim1 in index_of_bands:
|
||
j0 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_kx[:, dim1]), vector_delta_kx_ky[:, dim2])
|
||
j0 += 1
|
||
i0 += 1
|
||
dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
|
||
det_value = det_value*dot_matrix
|
||
# third dot product
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i0 = 0
|
||
for dim1 in index_of_bands:
|
||
j0 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_kx_ky[:, dim1]), vector_delta_ky[:, dim2])
|
||
j0 += 1
|
||
i0 += 1
|
||
dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
|
||
det_value = det_value*dot_matrix
|
||
# four dot product
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i0 = 0
|
||
for dim1 in index_of_bands:
|
||
j0 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_ky[:, dim1]), vector[:, dim2])
|
||
j0 += 1
|
||
i0 += 1
|
||
dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
|
||
det_value= det_value*dot_matrix
|
||
chern_number += cmath.log(det_value)
|
||
chern_number = chern_number/(2*math.pi*1j)
|
||
return chern_number
|
||
|
||
# 通过Wilson loop方法计算方格子的陈数
|
||
def calculate_chern_number_for_square_lattice_with_wilson_loop(hamiltonian_function, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0):
|
||
delta = 2*math.pi/precision_of_plaquettes
|
||
chern_number = 0
|
||
for kx in np.arange(-math.pi, math.pi, delta):
|
||
if print_show == 1:
|
||
print(kx)
|
||
for ky in np.arange(-math.pi, math.pi, delta):
|
||
vector_array = []
|
||
# line_1
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_2
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_3
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_4
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
wilson_loop = 1
|
||
for i0 in range(len(vector_array)-1):
|
||
wilson_loop = wilson_loop*np.dot(vector_array[i0].transpose().conj(), vector_array[i0+1])
|
||
wilson_loop = wilson_loop*np.dot(vector_array[len(vector_array)-1].transpose().conj(), vector_array[0])
|
||
arg = np.log(np.diagonal(wilson_loop))/1j
|
||
chern_number = chern_number + arg
|
||
chern_number = chern_number/(2*math.pi)
|
||
return chern_number
|
||
|
||
# 通过Wilson loop方法计算方格子的陈数（可计算简并的情况）
|
||
def calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0):
|
||
delta = 2*math.pi/precision_of_plaquettes
|
||
chern_number = 0
|
||
for kx in np.arange(-math.pi, math.pi, delta):
|
||
if print_show == 1:
|
||
print(kx)
|
||
for ky in np.arange(-math.pi, math.pi, delta):
|
||
vector_array = []
|
||
# line_1
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_2
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_3
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_4
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
wilson_loop = 1
|
||
dim = len(index_of_bands)
|
||
for i0 in range(len(vector_array)-1):
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i01 = 0
|
||
for dim1 in index_of_bands:
|
||
i02 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i01, i02] = np.dot(vector_array[i0][:, dim1].transpose().conj(), vector_array[i0+1][:, dim2])
|
||
i02 += 1
|
||
i01 += 1
|
||
det_value = np.linalg.det(dot_matrix)
|
||
wilson_loop = wilson_loop*det_value
|
||
dot_matrix_plus = np.zeros((dim , dim), dtype=complex)
|
||
i01 = 0
|
||
for dim1 in index_of_bands:
|
||
i02 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix_plus[i01, i02] = np.dot(vector_array[len(vector_array)-1][:, dim1].transpose().conj(), vector_array[0][:, dim2])
|
||
i02 += 1
|
||
i01 += 1
|
||
det_value = np.linalg.det(dot_matrix_plus)
|
||
wilson_loop = wilson_loop*det_value
|
||
arg = np.log(wilson_loop)/1j
|
||
chern_number = chern_number + arg
|
||
chern_number = chern_number/(2*math.pi)
|
||
return chern_number
|
||
|
||
# 通过高效法计算贝利曲率
|
||
def calculate_berry_curvature_with_efficient_method(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision=100, print_show=0):
|
||
if np.array(hamiltonian_function(0, 0)).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(hamiltonian_function(0, 0)).shape[0]
|
||
delta = (k_max-k_min)/precision
|
||
k_array = np.arange(k_min, k_max, delta)
|
||
berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0], dim), dtype=complex)
|
||
i0 = 0
|
||
for kx in k_array:
|
||
if print_show == 1:
|
||
print(kx)
|
||
j0 = 0
|
||
for ky in k_array:
|
||
H = hamiltonian_function(kx, ky)
|
||
vector = guan.calculate_eigenvector(H)
|
||
H_delta_kx = hamiltonian_function(kx+delta, ky)
|
||
vector_delta_kx = guan.calculate_eigenvector(H_delta_kx)
|
||
H_delta_ky = hamiltonian_function(kx, ky+delta)
|
||
vector_delta_ky = guan.calculate_eigenvector(H_delta_ky)
|
||
H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
|
||
vector_delta_kx_ky = guan.calculate_eigenvector(H_delta_kx_ky)
|
||
for i in range(dim):
|
||
vector_i = vector[:, i]
|
||
vector_delta_kx_i = vector_delta_kx[:, i]
|
||
vector_delta_ky_i = vector_delta_ky[:, i]
|
||
vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
|
||
Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
|
||
Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
|
||
Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
|
||
Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
|
||
berry_curvature = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))/delta/delta*1j
|
||
berry_curvature_array[j0, i0, i] = berry_curvature
|
||
j0 += 1
|
||
i0 += 1
|
||
return k_array, berry_curvature_array
|
||
|
||
# 通过高效法计算贝利曲率（可计算简并的情况）
|
||
def calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min=-math.pi, k_max=math.pi, precision=100, print_show=0):
|
||
delta = (k_max-k_min)/precision
|
||
k_array = np.arange(k_min, k_max, delta)
|
||
berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0]), dtype=complex)
|
||
i00 = 0
|
||
for kx in np.arange(k_min, k_max, delta):
|
||
if print_show == 1:
|
||
print(kx)
|
||
j00 = 0
|
||
for ky in np.arange(k_min, k_max, delta):
|
||
H = hamiltonian_function(kx, ky)
|
||
eigenvalue, vector = np.linalg.eigh(H)
|
||
H_delta_kx = hamiltonian_function(kx+delta, ky)
|
||
eigenvalue, vector_delta_kx = np.linalg.eigh(H_delta_kx)
|
||
H_delta_ky = hamiltonian_function(kx, ky+delta)
|
||
eigenvalue, vector_delta_ky = np.linalg.eigh(H_delta_ky)
|
||
H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
|
||
eigenvalue, vector_delta_kx_ky = np.linalg.eigh(H_delta_kx_ky)
|
||
dim = len(index_of_bands)
|
||
det_value = 1
|
||
# first dot product
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i0 = 0
|
||
for dim1 in index_of_bands:
|
||
j0 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i0, j0] = np.dot(np.conj(vector[:, dim1]), vector_delta_kx[:, dim2])
|
||
j0 += 1
|
||
i0 += 1
|
||
dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
|
||
det_value = det_value*dot_matrix
|
||
# second dot product
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i0 = 0
|
||
for dim1 in index_of_bands:
|
||
j0 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_kx[:, dim1]), vector_delta_kx_ky[:, dim2])
|
||
j0 += 1
|
||
i0 += 1
|
||
dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
|
||
det_value = det_value*dot_matrix
|
||
# third dot product
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i0 = 0
|
||
for dim1 in index_of_bands:
|
||
j0 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_kx_ky[:, dim1]), vector_delta_ky[:, dim2])
|
||
j0 += 1
|
||
i0 += 1
|
||
dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
|
||
det_value = det_value*dot_matrix
|
||
# four dot product
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i0 = 0
|
||
for dim1 in index_of_bands:
|
||
j0 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i0, j0] = np.dot(np.conj(vector_delta_ky[:, dim1]), vector[:, dim2])
|
||
j0 += 1
|
||
i0 += 1
|
||
dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
|
||
det_value= det_value*dot_matrix
|
||
berry_curvature = cmath.log(det_value)/delta/delta*1j
|
||
berry_curvature_array[j00, i00] = berry_curvature
|
||
j00 += 1
|
||
i00 += 1
|
||
return k_array, berry_curvature_array
|
||
|
||
# 通过Wilson loop方法计算贝里曲率
|
||
def calculate_berry_curvature_with_wilson_loop(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0):
|
||
if np.array(hamiltonian_function(0, 0)).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(hamiltonian_function(0, 0)).shape[0]
|
||
delta = (k_max-k_min)/precision_of_plaquettes
|
||
k_array = np.arange(k_min, k_max, delta)
|
||
berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0], dim), dtype=complex)
|
||
i00 = 0
|
||
for kx in k_array:
|
||
if print_show == 1:
|
||
print(kx)
|
||
j00 = 0
|
||
for ky in k_array:
|
||
vector_array = []
|
||
# line_1
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_2
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_3
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_4
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
wilson_loop = 1
|
||
for i0 in range(len(vector_array)-1):
|
||
wilson_loop = wilson_loop*np.dot(vector_array[i0].transpose().conj(), vector_array[i0+1])
|
||
wilson_loop = wilson_loop*np.dot(vector_array[len(vector_array)-1].transpose().conj(), vector_array[0])
|
||
berry_curvature = np.log(np.diagonal(wilson_loop))/delta/delta*1j
|
||
berry_curvature_array[j00, i00, :]=berry_curvature
|
||
j00 += 1
|
||
i00 += 1
|
||
return k_array, berry_curvature_array
|
||
|
||
# 通过Wilson loop方法计算贝里曲率（可计算简并的情况）
|
||
def calculate_berry_curvature_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min=-math.pi, k_max=math.pi, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0):
|
||
delta = (k_max-k_min)/precision_of_plaquettes
|
||
k_array = np.arange(k_min, k_max, delta)
|
||
berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0]), dtype=complex)
|
||
i000 = 0
|
||
for kx in k_array:
|
||
if print_show == 1:
|
||
print(kx)
|
||
j000 = 0
|
||
for ky in k_array:
|
||
vector_array = []
|
||
# line_1
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_2
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_3
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
# line_4
|
||
for i0 in range(precision_of_wilson_loop):
|
||
H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)
|
||
eigenvalue, eigenvector = np.linalg.eig(H_delta)
|
||
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
|
||
vector_array.append(vector_delta)
|
||
wilson_loop = 1
|
||
dim = len(index_of_bands)
|
||
for i0 in range(len(vector_array)-1):
|
||
dot_matrix = np.zeros((dim , dim), dtype=complex)
|
||
i01 = 0
|
||
for dim1 in index_of_bands:
|
||
i02 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix[i01, i02] = np.dot(vector_array[i0][:, dim1].transpose().conj(), vector_array[i0+1][:, dim2])
|
||
i02 += 1
|
||
i01 += 1
|
||
det_value = np.linalg.det(dot_matrix)
|
||
wilson_loop = wilson_loop*det_value
|
||
dot_matrix_plus = np.zeros((dim , dim), dtype=complex)
|
||
i01 = 0
|
||
for dim1 in index_of_bands:
|
||
i02 = 0
|
||
for dim2 in index_of_bands:
|
||
dot_matrix_plus[i01, i02] = np.dot(vector_array[len(vector_array)-1][:, dim1].transpose().conj(), vector_array[0][:, dim2])
|
||
i02 += 1
|
||
i01 += 1
|
||
det_value = np.linalg.det(dot_matrix_plus)
|
||
wilson_loop = wilson_loop*det_value
|
||
berry_curvature = np.log(wilson_loop)/delta/delta*1j
|
||
berry_curvature_array[j000, i000]=berry_curvature
|
||
j000 += 1
|
||
i000 += 1
|
||
return k_array, berry_curvature_array
|
||
|
||
# 计算蜂窝格子的陈数（高效法）
|
||
def calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300, print_show=0):
|
||
if np.array(hamiltonian_function(0, 0)).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(hamiltonian_function(0, 0)).shape[0]
|
||
chern_number = np.zeros(dim, dtype=complex)
|
||
L1 = 4*math.sqrt(3)*math.pi/9/a
|
||
L2 = 2*math.sqrt(3)*math.pi/9/a
|
||
L3 = 2*math.pi/3/a
|
||
delta1 = 2*L1/precision
|
||
delta3 = 2*L3/precision
|
||
for kx in np.arange(-L1, L1, delta1):
|
||
if print_show == 1:
|
||
print(kx)
|
||
for ky in np.arange(-L3, L3, delta3):
|
||
if (-L2<=kx<=L2) or (kx>L2 and -(L1-kx)*math.tan(math.pi/3)<=ky<=(L1-kx)*math.tan(math.pi/3)) or (kx<-L2 and -(kx-(-L1))*math.tan(math.pi/3)<=ky<=(kx-(-L1))*math.tan(math.pi/3)):
|
||
H = hamiltonian_function(kx, ky)
|
||
vector = guan.calculate_eigenvector(H)
|
||
H_delta_kx = hamiltonian_function(kx+delta1, ky)
|
||
vector_delta_kx = guan.calculate_eigenvector(H_delta_kx)
|
||
H_delta_ky = hamiltonian_function(kx, ky+delta3)
|
||
vector_delta_ky = guan.calculate_eigenvector(H_delta_ky)
|
||
H_delta_kx_ky = hamiltonian_function(kx+delta1, ky+delta3)
|
||
vector_delta_kx_ky = guan.calculate_eigenvector(H_delta_kx_ky)
|
||
for i in range(dim):
|
||
vector_i = vector[:, i]
|
||
vector_delta_kx_i = vector_delta_kx[:, i]
|
||
vector_delta_ky_i = vector_delta_ky[:, i]
|
||
vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
|
||
Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
|
||
Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
|
||
Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
|
||
Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
|
||
F = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))
|
||
chern_number[i] = chern_number[i] + F
|
||
chern_number = chern_number/(2*math.pi*1j)
|
||
return chern_number
|
||
|
||
# 计算Wilson loop
|
||
def calculate_wilson_loop(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision=100, print_show=0):
|
||
k_array = np.linspace(k_min, k_max, precision)
|
||
dim = np.array(hamiltonian_function(0)).shape[0]
|
||
wilson_loop_array = np.ones(dim, dtype=complex)
|
||
for i in range(dim):
|
||
if print_show == 1:
|
||
print(i)
|
||
eigenvector_array = []
|
||
for k in k_array:
|
||
eigenvector = guan.calculate_eigenvector(hamiltonian_function(k))
|
||
if k != k_max:
|
||
eigenvector_array.append(eigenvector[:, i])
|
||
else:
|
||
eigenvector_array.append(eigenvector_array[0])
|
||
for i0 in range(precision-1):
|
||
F = np.dot(eigenvector_array[i0+1].transpose().conj(), eigenvector_array[i0])
|
||
wilson_loop_array[i] = np.dot(F, wilson_loop_array[i])
|
||
return wilson_loop_array
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 10: read and write
|
||
|
||
# 读取文件中的一维数据（每一行一组x和y）
|
||
def read_one_dimensional_data(filename='a', file_format='.txt'):
|
||
f = open(filename+file_format, 'r')
|
||
text = f.read()
|
||
f.close()
|
||
row_list = np.array(text.split('\n'))
|
||
dim_column = np.array(row_list[0].split()).shape[0]
|
||
x_array = np.array([])
|
||
y_array = np.array([])
|
||
for row in row_list:
|
||
column = np.array(row.split())
|
||
if column.shape[0] != 0:
|
||
x_array = np.append(x_array, [float(column[0])], axis=0)
|
||
y_row = np.zeros(dim_column-1)
|
||
for dim0 in range(dim_column-1):
|
||
y_row[dim0] = float(column[dim0+1])
|
||
if np.array(y_array).shape[0] == 0:
|
||
y_array = [y_row]
|
||
else:
|
||
y_array = np.append(y_array, [y_row], axis=0)
|
||
return x_array, y_array
|
||
|
||
# 读取文件中的一维数据（每一行一组x和y）（支持复数形式）
|
||
def read_one_dimensional_complex_data(filename='a', file_format='.txt'):
|
||
f = open(filename+file_format, 'r')
|
||
text = f.read()
|
||
f.close()
|
||
row_list = np.array(text.split('\n'))
|
||
dim_column = np.array(row_list[0].split()).shape[0]
|
||
x_array = np.array([])
|
||
y_array = np.array([])
|
||
for row in row_list:
|
||
column = np.array(row.split())
|
||
if column.shape[0] != 0:
|
||
x_array = np.append(x_array, [complex(column[0])], axis=0)
|
||
y_row = np.zeros(dim_column-1, dtype=complex)
|
||
for dim0 in range(dim_column-1):
|
||
y_row[dim0] = complex(column[dim0+1])
|
||
if np.array(y_array).shape[0] == 0:
|
||
y_array = [y_row]
|
||
else:
|
||
y_array = np.append(y_array, [y_row], axis=0)
|
||
return x_array, y_array
|
||
|
||
# 读取文件中的二维数据（第一行和列分别为横纵坐标）
|
||
def read_two_dimensional_data(filename='a', file_format='.txt'):
|
||
f = open(filename+file_format, 'r')
|
||
text = f.read()
|
||
f.close()
|
||
row_list = np.array(text.split('\n'))
|
||
dim_column = np.array(row_list[0].split()).shape[0]
|
||
x_array = np.array([])
|
||
y_array = np.array([])
|
||
matrix = np.array([])
|
||
for i0 in range(row_list.shape[0]):
|
||
column = np.array(row_list[i0].split())
|
||
if i0 == 0:
|
||
x_str = column[1::]
|
||
x_array = np.zeros(x_str.shape[0])
|
||
for i00 in range(x_str.shape[0]):
|
||
x_array[i00] = float(x_str[i00])
|
||
elif column.shape[0] != 0:
|
||
y_array = np.append(y_array, [float(column[0])], axis=0)
|
||
matrix_row = np.zeros(dim_column-1)
|
||
for dim0 in range(dim_column-1):
|
||
matrix_row[dim0] = float(column[dim0+1])
|
||
if np.array(matrix).shape[0] == 0:
|
||
matrix = [matrix_row]
|
||
else:
|
||
matrix = np.append(matrix, [matrix_row], axis=0)
|
||
return x_array, y_array, matrix
|
||
|
||
# 读取文件中的二维数据（第一行和列分别为横纵坐标）（支持复数形式）
|
||
def read_two_dimensional_complex_data(filename='a', file_format='.txt'):
|
||
f = open(filename+file_format, 'r')
|
||
text = f.read()
|
||
f.close()
|
||
row_list = np.array(text.split('\n'))
|
||
dim_column = np.array(row_list[0].split()).shape[0]
|
||
x_array = np.array([])
|
||
y_array = np.array([])
|
||
matrix = np.array([])
|
||
for i0 in range(row_list.shape[0]):
|
||
column = np.array(row_list[i0].split())
|
||
if i0 == 0:
|
||
x_str = column[1::]
|
||
x_array = np.zeros(x_str.shape[0], dtype=complex)
|
||
for i00 in range(x_str.shape[0]):
|
||
x_array[i00] = complex(x_str[i00])
|
||
elif column.shape[0] != 0:
|
||
y_array = np.append(y_array, [complex(column[0])], axis=0)
|
||
matrix_row = np.zeros(dim_column-1, dtype=complex)
|
||
for dim0 in range(dim_column-1):
|
||
matrix_row[dim0] = complex(column[dim0+1])
|
||
if np.array(matrix).shape[0] == 0:
|
||
matrix = [matrix_row]
|
||
else:
|
||
matrix = np.append(matrix, [matrix_row], axis=0)
|
||
return x_array, y_array, matrix
|
||
|
||
# 读取文件中的二维数据（不包括x和y）
|
||
def read_two_dimensional_data_without_xy_array(filename='a', file_format='.txt'):
|
||
matrix = np.loadtxt(filename+file_format)
|
||
return matrix
|
||
|
||
# 打开文件用于新增内容
|
||
def open_file(filename='a', file_format='.txt'):
|
||
try:
|
||
f = open(filename+file_format, 'a', encoding='UTF-8')
|
||
except:
|
||
f = open(filename+file_format, 'w', encoding='UTF-8')
|
||
return f
|
||
|
||
# 在文件中写入一维数据（每一行一组x和y）
|
||
def write_one_dimensional_data(x_array, y_array, filename='a', file_format='.txt'):
|
||
with open(filename+file_format, 'w', encoding='UTF-8') as f:
|
||
guan.write_one_dimensional_data_without_opening_file(x_array, y_array, f)
|
||
|
||
# 在文件中写入一维数据（每一行一组x和y）（需要输入文件）
|
||
def write_one_dimensional_data_without_opening_file(x_array, y_array, f):
|
||
x_array = np.array(x_array)
|
||
y_array = np.array(y_array)
|
||
i0 = 0
|
||
for x0 in x_array:
|
||
f.write(str(x0)+' ')
|
||
if len(y_array.shape) == 1:
|
||
f.write(str(y_array[i0])+'\n')
|
||
elif len(y_array.shape) == 2:
|
||
for j0 in range(y_array.shape[1]):
|
||
f.write(str(y_array[i0, j0])+' ')
|
||
f.write('\n')
|
||
i0 += 1
|
||
|
||
# 在文件中写入二维数据（第一行和列分别为横纵坐标）
|
||
def write_two_dimensional_data(x_array, y_array, matrix, filename='a', file_format='.txt'):
|
||
with open(filename+file_format, 'w', encoding='UTF-8') as f:
|
||
guan.write_two_dimensional_data_without_opening_file(x_array, y_array, matrix, f)
|
||
|
||
# 在文件中写入二维数据（第一行和列分别为横纵坐标）（需要输入文件）
|
||
def write_two_dimensional_data_without_opening_file(x_array, y_array, matrix, f):
|
||
x_array = np.array(x_array)
|
||
y_array = np.array(y_array)
|
||
matrix = np.array(matrix)
|
||
f.write('0 ')
|
||
for x0 in x_array:
|
||
f.write(str(x0)+' ')
|
||
f.write('\n')
|
||
i0 = 0
|
||
for y0 in y_array:
|
||
f.write(str(y0))
|
||
j0 = 0
|
||
for x0 in x_array:
|
||
f.write(' '+str(matrix[i0, j0])+' ')
|
||
j0 += 1
|
||
f.write('\n')
|
||
i0 += 1
|
||
|
||
# 在文件中写入二维数据（不包括x和y）
|
||
def write_two_dimensional_data_without_xy_array(matrix, filename='a', file_format='.txt'):
|
||
with open(filename+file_format, 'w', encoding='UTF-8') as f:
|
||
guan.write_two_dimensional_data_without_xy_array_and_without_opening_file(matrix, f)
|
||
|
||
# 在文件中写入二维数据（不包括x和y）（需要输入文件）
|
||
def write_two_dimensional_data_without_xy_array_and_without_opening_file(matrix, f):
|
||
for row in matrix:
|
||
for element in row:
|
||
f.write(str(element)+' ')
|
||
f.write('\n')
|
||
|
||
# 以显示编号的样式，打印数组
|
||
def print_array_with_index(array, show_index=1, index_type=0):
|
||
if show_index==0:
|
||
for i0 in array:
|
||
print(i0)
|
||
else:
|
||
if index_type==0:
|
||
index = 0
|
||
for i0 in array:
|
||
print(index, i0)
|
||
index += 1
|
||
else:
|
||
index = 0
|
||
for i0 in array:
|
||
index += 1
|
||
print(index, i0)
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 11: plot figures
|
||
|
||
# 导入plt, fig, ax
|
||
def import_plt_and_start_fig_ax(adjust_bottom=0.2, adjust_left=0.2, labelsize=20):
|
||
import matplotlib.pyplot as plt
|
||
fig, ax = plt.subplots()
|
||
plt.subplots_adjust(bottom=adjust_bottom, left=adjust_left)
|
||
ax.grid()
|
||
ax.tick_params(labelsize=labelsize)
|
||
labels = ax.get_xticklabels() + ax.get_yticklabels()
|
||
[label.set_fontname('Times New Roman') for label in labels]
|
||
return plt, fig, ax
|
||
|
||
# 基于plt, fig, ax开始画图
|
||
def plot_without_starting_fig(plt, fig, ax, x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, style='', y_min=None, y_max=None, linewidth=None, markersize=None, color=None):
|
||
if color==None:
|
||
ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize)
|
||
else:
|
||
ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize, color=color)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
if y_min!=None or y_max!=None:
|
||
if y_min==None:
|
||
y_min=min(y_array)
|
||
if y_max==None:
|
||
y_max=max(y_array)
|
||
ax.set_ylim(y_min, y_max)
|
||
|
||
# 画图
|
||
def plot(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style='', y_min=None, y_max=None, linewidth=None, markersize=None, adjust_bottom=0.2, adjust_left=0.2):
|
||
plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize)
|
||
ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
if y_min!=None or y_max!=None:
|
||
if y_min==None:
|
||
y_min=min(y_array)
|
||
if y_max==None:
|
||
y_max=max(y_array)
|
||
ax.set_ylim(y_min, y_max)
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
if show == 1:
|
||
plt.show()
|
||
plt.close('all')
|
||
|
||
# 一组横坐标数据，两组纵坐标数据画图
|
||
def plot_two_array(x_array, y1_array, y2_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style_1='', style_2='', y_min=None, y_max=None, linewidth_1=None, linewidth_2=None, markersize_1=None, markersize_2=None, adjust_bottom=0.2, adjust_left=0.2):
|
||
plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize)
|
||
ax.plot(x_array, y1_array, style_1, linewidth=linewidth_1, markersize=markersize_1)
|
||
ax.plot(x_array, y2_array, style_2, linewidth=linewidth_2, markersize=markersize_2)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
if y_min!=None or y_max!=None:
|
||
if y_min==None:
|
||
y1_min=min(y1_array)
|
||
y2_min=min(y2_array)
|
||
y_min=min([y1_min, y2_min])
|
||
if y_max==None:
|
||
y1_max=max(y1_array)
|
||
y2_max=max(y2_array)
|
||
y_max=max([y1_max, y2_max])
|
||
ax.set_ylim(y_min, y_max)
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
if show == 1:
|
||
plt.show()
|
||
plt.close('all')
|
||
|
||
# 两组横坐标数据，两组纵坐标数据画图
|
||
def plot_two_array_with_two_horizontal_array(x1_array, x2_array, y1_array, y2_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style_1='', style_2='', y_min=None, y_max=None, linewidth_1=None, linewidth_2=None, markersize_1=None, markersize_2=None, adjust_bottom=0.2, adjust_left=0.2):
|
||
plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize)
|
||
ax.plot(x1_array, y1_array, style_1, linewidth=linewidth_1, markersize=markersize_1)
|
||
ax.plot(x2_array, y2_array, style_2, linewidth=linewidth_2, markersize=markersize_2)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
if y_min!=None or y_max!=None:
|
||
if y_min==None:
|
||
y1_min=min(y1_array)
|
||
y2_min=min(y2_array)
|
||
y_min=min([y1_min, y2_min])
|
||
if y_max==None:
|
||
y1_max=max(y1_array)
|
||
y2_max=max(y2_array)
|
||
y_max=max([y1_max, y2_max])
|
||
ax.set_ylim(y_min, y_max)
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
if show == 1:
|
||
plt.show()
|
||
plt.close('all')
|
||
|
||
# 一组横坐标数据，三组纵坐标数据画图
|
||
def plot_three_array(x_array, y1_array, y2_array, y3_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style_1='', style_2='', style_3='', y_min=None, y_max=None, linewidth_1=None, linewidth_2=None, linewidth_3=None,markersize_1=None, markersize_2=None, markersize_3=None, adjust_bottom=0.2, adjust_left=0.2):
|
||
plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize)
|
||
ax.plot(x_array, y1_array, style_1, linewidth=linewidth_1, markersize=markersize_1)
|
||
ax.plot(x_array, y2_array, style_2, linewidth=linewidth_2, markersize=markersize_2)
|
||
ax.plot(x_array, y3_array, style_3, linewidth=linewidth_3, markersize=markersize_3)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
if y_min!=None or y_max!=None:
|
||
if y_min==None:
|
||
y1_min=min(y1_array)
|
||
y2_min=min(y2_array)
|
||
y3_min=min(y3_array)
|
||
y_min=min([y1_min, y2_min, y3_min])
|
||
if y_max==None:
|
||
y1_max=max(y1_array)
|
||
y2_max=max(y2_array)
|
||
y3_max=max(y3_array)
|
||
y_max=max([y1_max, y2_max, y3_max])
|
||
ax.set_ylim(y_min, y_max)
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
if show == 1:
|
||
plt.show()
|
||
plt.close('all')
|
||
|
||
# 三组横坐标数据，三组纵坐标数据画图
|
||
def plot_three_array_with_three_horizontal_array(x1_array, x2_array, x3_array, y1_array, y2_array, y3_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style_1='', style_2='', style_3='', y_min=None, y_max=None, linewidth_1=None, linewidth_2=None, linewidth_3=None,markersize_1=None, markersize_2=None, markersize_3=None, adjust_bottom=0.2, adjust_left=0.2):
|
||
plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize)
|
||
ax.plot(x1_array, y1_array, style_1, linewidth=linewidth_1, markersize=markersize_1)
|
||
ax.plot(x2_array, y2_array, style_2, linewidth=linewidth_2, markersize=markersize_2)
|
||
ax.plot(x3_array, y3_array, style_3, linewidth=linewidth_3, markersize=markersize_3)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
if y_min!=None or y_max!=None:
|
||
if y_min==None:
|
||
y1_min=min(y1_array)
|
||
y2_min=min(y2_array)
|
||
y3_min=min(y3_array)
|
||
y_min=min([y1_min, y2_min, y3_min])
|
||
if y_max==None:
|
||
y1_max=max(y1_array)
|
||
y2_max=max(y2_array)
|
||
y3_max=max(y3_array)
|
||
y_max=max([y1_max, y2_max, y3_max])
|
||
ax.set_ylim(y_min, y_max)
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
if show == 1:
|
||
plt.show()
|
||
plt.close('all')
|
||
|
||
# 画三维图
|
||
def plot_3d_surface(x_array, y_array, matrix, xlabel='x', ylabel='y', zlabel='z', title='', fontsize=20, labelsize=15, show=1, save=0, filename='a', file_format='.jpg', dpi=300, z_min=None, z_max=None, rcount=100, ccount=100):
|
||
import matplotlib.pyplot as plt
|
||
from matplotlib import cm
|
||
from matplotlib.ticker import LinearLocator
|
||
matrix = np.array(matrix)
|
||
fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
|
||
plt.subplots_adjust(bottom=0.1, right=0.65)
|
||
x_array, y_array = np.meshgrid(x_array, y_array)
|
||
if len(matrix.shape) == 2:
|
||
surf = ax.plot_surface(x_array, y_array, matrix, rcount=rcount, ccount=ccount, cmap=cm.coolwarm, linewidth=0, antialiased=False)
|
||
elif len(matrix.shape) == 3:
|
||
for i0 in range(matrix.shape[2]):
|
||
surf = ax.plot_surface(x_array, y_array, matrix[:,:,i0], rcount=rcount, ccount=ccount, cmap=cm.coolwarm, linewidth=0, antialiased=False)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_zlabel(zlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.zaxis.set_major_locator(LinearLocator(5))
|
||
ax.zaxis.set_major_formatter('{x:.2f}')
|
||
if z_min!=None or z_max!=None:
|
||
if z_min==None:
|
||
z_min=matrix.min()
|
||
if z_max==None:
|
||
z_max=matrix.max()
|
||
ax.set_zlim(z_min, z_max)
|
||
ax.tick_params(labelsize=labelsize)
|
||
labels = ax.get_xticklabels() + ax.get_yticklabels() + ax.get_zticklabels()
|
||
[label.set_fontname('Times New Roman') for label in labels]
|
||
cax = plt.axes([0.8, 0.1, 0.05, 0.8])
|
||
cbar = fig.colorbar(surf, cax=cax)
|
||
cbar.ax.tick_params(labelsize=labelsize)
|
||
for l in cbar.ax.yaxis.get_ticklabels():
|
||
l.set_family('Times New Roman')
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
if show == 1:
|
||
plt.show()
|
||
plt.close('all')
|
||
|
||
# 画Contour图
|
||
def plot_contour(x_array, y_array, matrix, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=15, cmap='jet', levels=None, show=1, save=0, filename='a', file_format='.jpg', dpi=300):
|
||
import matplotlib.pyplot as plt
|
||
fig, ax = plt.subplots()
|
||
plt.subplots_adjust(bottom=0.2, right=0.75, left=0.2)
|
||
x_array, y_array = np.meshgrid(x_array, y_array)
|
||
contour = ax.contourf(x_array,y_array,matrix,cmap=cmap, levels=levels)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.tick_params(labelsize=labelsize)
|
||
labels = ax.get_xticklabels() + ax.get_yticklabels()
|
||
[label.set_fontname('Times New Roman') for label in labels]
|
||
cax = plt.axes([0.8, 0.2, 0.05, 0.68])
|
||
cbar = fig.colorbar(contour, cax=cax)
|
||
cbar.ax.tick_params(labelsize=labelsize)
|
||
for l in cbar.ax.yaxis.get_ticklabels():
|
||
l.set_family('Times New Roman')
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
if show == 1:
|
||
plt.show()
|
||
plt.close('all')
|
||
|
||
# 画棋盘图/伪彩色图
|
||
def plot_pcolor(x_array, y_array, matrix, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=15, cmap='jet', levels=None, show=1, save=0, filename='a', file_format='.jpg', dpi=300):
|
||
import matplotlib.pyplot as plt
|
||
fig, ax = plt.subplots()
|
||
plt.subplots_adjust(bottom=0.2, right=0.75, left=0.2)
|
||
x_array, y_array = np.meshgrid(x_array, y_array)
|
||
contour = ax.pcolor(x_array,y_array,matrix, cmap=cmap)
|
||
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
|
||
ax.tick_params(labelsize=labelsize)
|
||
labels = ax.get_xticklabels() + ax.get_yticklabels()
|
||
[label.set_fontname('Times New Roman') for label in labels]
|
||
cax = plt.axes([0.8, 0.2, 0.05, 0.68])
|
||
cbar = fig.colorbar(contour, cax=cax)
|
||
cbar.ax.tick_params(labelsize=labelsize)
|
||
for l in cbar.ax.yaxis.get_ticklabels():
|
||
l.set_family('Times New Roman')
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
if show == 1:
|
||
plt.show()
|
||
plt.close('all')
|
||
|
||
# 通过坐标画点和线
|
||
def draw_dots_and_lines(coordinate_array, draw_dots=1, draw_lines=1, max_distance=1.1, line_style='-k', linewidth=1, dot_style='ro', markersize=3, show=1, save=0, filename='a', file_format='.eps', dpi=300):
|
||
import matplotlib.pyplot as plt
|
||
coordinate_array = np.array(coordinate_array)
|
||
print(coordinate_array.shape)
|
||
x_range = max(coordinate_array[:, 0])-min(coordinate_array[:, 0])
|
||
y_range = max(coordinate_array[:, 1])-min(coordinate_array[:, 1])
|
||
fig, ax = plt.subplots(figsize=(6*x_range/y_range,6))
|
||
plt.subplots_adjust(left=0, bottom=0, right=1, top=1)
|
||
plt.axis('off')
|
||
if draw_lines==1:
|
||
for i1 in range(coordinate_array.shape[0]):
|
||
for i2 in range(coordinate_array.shape[0]):
|
||
if np.sqrt((coordinate_array[i1, 0] - coordinate_array[i2, 0])**2+(coordinate_array[i1, 1] - coordinate_array[i2, 1])**2) < max_distance:
|
||
ax.plot([coordinate_array[i1, 0], coordinate_array[i2, 0]], [coordinate_array[i1, 1], coordinate_array[i2, 1]], line_style, linewidth=linewidth)
|
||
if draw_dots==1:
|
||
for i in range(coordinate_array.shape[0]):
|
||
ax.plot(coordinate_array[i, 0], coordinate_array[i, 1], dot_style, markersize=markersize)
|
||
if show==1:
|
||
plt.show()
|
||
if save==1:
|
||
if file_format=='.eps':
|
||
plt.savefig(filename+file_format)
|
||
else:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
|
||
# 合并两个图片
|
||
def combine_two_images(image_path_array, figsize=(16,8), show=0, save=1, filename='a', file_format='.jpg', dpi=300):
|
||
num = np.array(image_path_array).shape[0]
|
||
if num != 2:
|
||
print('Error: The number of images should be two!')
|
||
else:
|
||
import matplotlib.pyplot as plt
|
||
import matplotlib.image as mpimg
|
||
fig = plt.figure(figsize=figsize)
|
||
plt.subplots_adjust(left=0, right=1, bottom=0, top=1, wspace=0, hspace=0)
|
||
ax1 = fig.add_subplot(121)
|
||
ax2 = fig.add_subplot(122)
|
||
image_1 = mpimg.imread(image_path_array[0])
|
||
image_2 = mpimg.imread(image_path_array[1])
|
||
ax1.imshow(image_1)
|
||
ax2.imshow(image_2)
|
||
ax1.axis('off')
|
||
ax2.axis('off')
|
||
if show == 1:
|
||
plt.show()
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
plt.close('all')
|
||
|
||
# 合并三个图片
|
||
def combine_three_images(image_path_array, figsize=(16,5), show=0, save=1, filename='a', file_format='.jpg', dpi=300):
|
||
num = np.array(image_path_array).shape[0]
|
||
if num != 3:
|
||
print('Error: The number of images should be three!')
|
||
else:
|
||
import matplotlib.pyplot as plt
|
||
import matplotlib.image as mpimg
|
||
fig = plt.figure(figsize=figsize)
|
||
plt.subplots_adjust(left=0, right=1, bottom=0, top=1, wspace=0, hspace=0)
|
||
ax1 = fig.add_subplot(131)
|
||
ax2 = fig.add_subplot(132)
|
||
ax3 = fig.add_subplot(133)
|
||
image_1 = mpimg.imread(image_path_array[0])
|
||
image_2 = mpimg.imread(image_path_array[1])
|
||
image_3 = mpimg.imread(image_path_array[2])
|
||
ax1.imshow(image_1)
|
||
ax2.imshow(image_2)
|
||
ax3.imshow(image_3)
|
||
ax1.axis('off')
|
||
ax2.axis('off')
|
||
ax3.axis('off')
|
||
if show == 1:
|
||
plt.show()
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
plt.close('all')
|
||
|
||
# 合并四个图片
|
||
def combine_four_images(image_path_array, figsize=(16,16), show=0, save=1, filename='a', file_format='.jpg', dpi=300):
|
||
num = np.array(image_path_array).shape[0]
|
||
if num != 4:
|
||
print('Error: The number of images should be four!')
|
||
else:
|
||
import matplotlib.pyplot as plt
|
||
import matplotlib.image as mpimg
|
||
fig = plt.figure(figsize=figsize)
|
||
plt.subplots_adjust(left=0, right=1, bottom=0, top=1, wspace=0, hspace=0)
|
||
ax1 = fig.add_subplot(221)
|
||
ax2 = fig.add_subplot(222)
|
||
ax3 = fig.add_subplot(223)
|
||
ax4 = fig.add_subplot(224)
|
||
image_1 = mpimg.imread(image_path_array[0])
|
||
image_2 = mpimg.imread(image_path_array[1])
|
||
image_3 = mpimg.imread(image_path_array[2])
|
||
image_4 = mpimg.imread(image_path_array[3])
|
||
ax1.imshow(image_1)
|
||
ax2.imshow(image_2)
|
||
ax3.imshow(image_3)
|
||
ax4.imshow(image_4)
|
||
ax1.axis('off')
|
||
ax2.axis('off')
|
||
ax3.axis('off')
|
||
ax4.axis('off')
|
||
if show == 1:
|
||
plt.show()
|
||
if save == 1:
|
||
plt.savefig(filename+file_format, dpi=dpi)
|
||
plt.close('all')
|
||
|
||
# 制作GIF动画
|
||
def make_gif(image_path_array, filename='a', duration=0.1):
|
||
import imageio
|
||
images = []
|
||
for image_path in image_path_array:
|
||
im = imageio.imread(image_path)
|
||
images.append(im)
|
||
imageio.mimsave(filename+'.gif', images, 'GIF', duration=duration)
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 12: data processing
|
||
|
||
# 并行计算前的预处理，把参数分成多份
|
||
def preprocess_for_parallel_calculations(parameter_array_all, cpus=1, task_index=0):
|
||
num_all = np.array(parameter_array_all).shape[0]
|
||
if num_all%cpus == 0:
|
||
num_parameter = int(num_all/cpus)
|
||
parameter_array = parameter_array_all[task_index*num_parameter:(task_index+1)*num_parameter]
|
||
else:
|
||
num_parameter = int(num_all/(cpus-1))
|
||
if task_index != cpus-1:
|
||
parameter_array = parameter_array_all[task_index*num_parameter:(task_index+1)*num_parameter]
|
||
else:
|
||
parameter_array = parameter_array_all[task_index*num_parameter:num_all]
|
||
return parameter_array
|
||
|
||
# 在一组数据中找到数值相近的数
|
||
def find_close_values_in_one_array(array, precision=1e-2):
|
||
new_array = []
|
||
i0 = 0
|
||
for a1 in array:
|
||
j0 = 0
|
||
for a2 in array:
|
||
if j0>i0 and abs(a1-a2)<precision:
|
||
new_array.append([a1, a2])
|
||
j0 +=1
|
||
i0 += 1
|
||
return new_array
|
||
|
||
# 寻找能带的简并点
|
||
def find_degenerate_points(k_array, eigenvalue_array, precision=1e-2):
|
||
degenerate_k_array = []
|
||
degenerate_eigenvalue_array = []
|
||
i0 = 0
|
||
for k in k_array:
|
||
degenerate_points = find_close_values_in_one_array(eigenvalue_array[i0], precision=precision)
|
||
if len(degenerate_points) != 0:
|
||
degenerate_k_array.append(k)
|
||
degenerate_eigenvalue_array.append(degenerate_points)
|
||
i0 += 1
|
||
return degenerate_k_array, degenerate_eigenvalue_array
|
||
|
||
# 对于某个目录中的txt文件，批量读取和画图
|
||
def batch_reading_and_plotting(directory, xlabel='x', ylabel='y'):
|
||
import re
|
||
import os
|
||
for root, dirs, files in os.walk(directory):
|
||
for file in files:
|
||
if re.search('^txt.', file[::-1]):
|
||
filename = file[:-4]
|
||
x_array, y_array = guan.read_one_dimensional_data(filename=filename)
|
||
guan.plot(x_array, y_array, xlabel=xlabel, ylabel=ylabel, title=filename, show=0, save=1, filename=filename)
|
||
|
||
# 将RGB转成HEX
|
||
def rgb_to_hex(rgb, pound=1):
|
||
if pound==0:
|
||
return '%02x%02x%02x' % rgb
|
||
else:
|
||
return '#%02x%02x%02x' % rgb
|
||
|
||
# 将HEX转成RGB
|
||
def hex_to_rgb(hex):
|
||
hex = hex.lstrip('#')
|
||
length = len(hex)
|
||
return tuple(int(hex[i:i+length//3], 16) for i in range(0, length, length//3))
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# # Module 13: file processing
|
||
|
||
# 将文件目录结构写入Markdown文件
|
||
def write_file_list_in_markdown(directory='./', filename='a', reverse_positive_or_negative=1, starting_from_h1=None, banned_file_format=[], hide_file_format=None, divided_line=None, show_second_number=None, show_third_number=None):
|
||
import os
|
||
f = open(filename+'.md', 'w', encoding="utf-8")
|
||
filenames1 = os.listdir(directory)
|
||
u0 = 0
|
||
for filename1 in filenames1[::reverse_positive_or_negative]:
|
||
filename1_with_path = os.path.join(directory,filename1)
|
||
if os.path.isfile(filename1_with_path):
|
||
if os.path.splitext(filename1)[1] not in banned_file_format:
|
||
if hide_file_format == None:
|
||
f.write('+ '+str(filename1)+'\n\n')
|
||
else:
|
||
f.write('+ '+str(os.path.splitext(filename1)[0])+'\n\n')
|
||
else:
|
||
u0 += 1
|
||
if divided_line != None and u0 != 1:
|
||
f.write('--------\n\n')
|
||
if starting_from_h1 == None:
|
||
f.write('#')
|
||
f.write('# '+str(filename1)+'\n\n')
|
||
|
||
filenames2 = os.listdir(filename1_with_path)
|
||
i0 = 0
|
||
for filename2 in filenames2[::reverse_positive_or_negative]:
|
||
filename2_with_path = os.path.join(directory, filename1, filename2)
|
||
if os.path.isfile(filename2_with_path):
|
||
if os.path.splitext(filename2)[1] not in banned_file_format:
|
||
if hide_file_format == None:
|
||
f.write('+ '+str(filename2)+'\n\n')
|
||
else:
|
||
f.write('+ '+str(os.path.splitext(filename2)[0])+'\n\n')
|
||
else:
|
||
i0 += 1
|
||
if starting_from_h1 == None:
|
||
f.write('#')
|
||
if show_second_number != None:
|
||
f.write('## '+str(i0)+'. '+str(filename2)+'\n\n')
|
||
else:
|
||
f.write('## '+str(filename2)+'\n\n')
|
||
|
||
j0 = 0
|
||
filenames3 = os.listdir(filename2_with_path)
|
||
for filename3 in filenames3[::reverse_positive_or_negative]:
|
||
filename3_with_path = os.path.join(directory, filename1, filename2, filename3)
|
||
if os.path.isfile(filename3_with_path):
|
||
if os.path.splitext(filename3)[1] not in banned_file_format:
|
||
if hide_file_format == None:
|
||
f.write('+ '+str(filename3)+'\n\n')
|
||
else:
|
||
f.write('+ '+str(os.path.splitext(filename3)[0])+'\n\n')
|
||
else:
|
||
j0 += 1
|
||
if starting_from_h1 == None:
|
||
f.write('#')
|
||
if show_third_number != None:
|
||
f.write('### ('+str(j0)+') '+str(filename3)+'\n\n')
|
||
else:
|
||
f.write('### '+str(filename3)+'\n\n')
|
||
|
||
filenames4 = os.listdir(filename3_with_path)
|
||
for filename4 in filenames4[::reverse_positive_or_negative]:
|
||
filename4_with_path = os.path.join(directory, filename1, filename2, filename3, filename4)
|
||
if os.path.isfile(filename4_with_path):
|
||
if os.path.splitext(filename4)[1] not in banned_file_format:
|
||
if hide_file_format == None:
|
||
f.write('+ '+str(filename4)+'\n\n')
|
||
else:
|
||
f.write('+ '+str(os.path.splitext(filename4)[0])+'\n\n')
|
||
else:
|
||
if starting_from_h1 == None:
|
||
f.write('#')
|
||
f.write('#### '+str(filename4)+'\n\n')
|
||
|
||
filenames5 = os.listdir(filename4_with_path)
|
||
for filename5 in filenames5[::reverse_positive_or_negative]:
|
||
filename5_with_path = os.path.join(directory, filename1, filename2, filename3, filename4, filename5)
|
||
if os.path.isfile(filename5_with_path):
|
||
if os.path.splitext(filename5)[1] not in banned_file_format:
|
||
if hide_file_format == None:
|
||
f.write('+ '+str(filename5)+'\n\n')
|
||
else:
|
||
f.write('+ '+str(os.path.splitext(filename5)[0])+'\n\n')
|
||
else:
|
||
if starting_from_h1 == None:
|
||
f.write('#')
|
||
f.write('##### '+str(filename5)+'\n\n')
|
||
|
||
filenames6 = os.listdir(filename5_with_path)
|
||
for filename6 in filenames6[::reverse_positive_or_negative]:
|
||
filename6_with_path = os.path.join(directory, filename1, filename2, filename3, filename4, filename5, filename6)
|
||
if os.path.isfile(filename6_with_path):
|
||
if os.path.splitext(filename6)[1] not in banned_file_format:
|
||
if hide_file_format == None:
|
||
f.write('+ '+str(filename6)+'\n\n')
|
||
else:
|
||
f.write('+ '+str(os.path.splitext(filename6)[0])+'\n\n')
|
||
else:
|
||
if starting_from_h1 == None:
|
||
f.write('#')
|
||
f.write('###### '+str(filename6)+'\n\n')
|
||
f.close()
|
||
|
||
# 查找文件名相同的文件
|
||
def find_repeated_file_with_same_filename(directory='./', ignored_directory_with_words=[], ignored_file_with_words=[], num=1000):
|
||
import os
|
||
from collections import Counter
|
||
file_list = []
|
||
for root, dirs, files in os.walk(directory):
|
||
for i0 in range(len(files)):
|
||
file_list.append(files[i0])
|
||
for word in ignored_directory_with_words:
|
||
if word in root:
|
||
file_list.remove(files[i0])
|
||
for word in ignored_file_with_words:
|
||
if word in files[i0]:
|
||
try:
|
||
file_list.remove(files[i0])
|
||
except:
|
||
pass
|
||
count_file = Counter(file_list).most_common(num)
|
||
repeated_file = []
|
||
for item in count_file:
|
||
if item[1]>1:
|
||
repeated_file.append(item)
|
||
return repeated_file
|
||
|
||
# 统计各个子文件夹中的文件数量
|
||
def count_file_in_sub_directory(directory='./', smaller_than_num=None):
|
||
import os
|
||
from collections import Counter
|
||
dirs_list = []
|
||
for root, dirs, files in os.walk(directory):
|
||
if dirs != []:
|
||
for i0 in range(len(dirs)):
|
||
dirs_list.append(root+'/'+dirs[i0])
|
||
for sub_dir in dirs_list:
|
||
file_list = []
|
||
for root, dirs, files in os.walk(sub_dir):
|
||
for i0 in range(len(files)):
|
||
file_list.append(files[i0])
|
||
count_file = len(file_list)
|
||
if smaller_than_num == None:
|
||
print(sub_dir)
|
||
print(count_file)
|
||
print()
|
||
else:
|
||
if count_file<smaller_than_num:
|
||
print(sub_dir)
|
||
print(count_file)
|
||
print()
|
||
|
||
# 产生必要的文件，例如readme.md
|
||
def creat_necessary_file(directory, filename='readme', file_format='.md', content='', overwrite=None, ignored_directory_with_words=[]):
|
||
import os
|
||
directory_with_file = []
|
||
ignored_directory = []
|
||
for root, dirs, files in os.walk(directory):
|
||
for i0 in range(len(files)):
|
||
if root not in directory_with_file:
|
||
directory_with_file.append(root)
|
||
if files[i0] == filename+file_format:
|
||
if root not in ignored_directory:
|
||
ignored_directory.append(root)
|
||
if overwrite == None:
|
||
for root in ignored_directory:
|
||
directory_with_file.remove(root)
|
||
ignored_directory_more =[]
|
||
for root in directory_with_file:
|
||
for word in ignored_directory_with_words:
|
||
if word in root:
|
||
if root not in ignored_directory_more:
|
||
ignored_directory_more.append(root)
|
||
for root in ignored_directory_more:
|
||
directory_with_file.remove(root)
|
||
for root in directory_with_file:
|
||
os.chdir(root)
|
||
f = open(filename+file_format, 'w', encoding="utf-8")
|
||
f.write(content)
|
||
f.close()
|
||
|
||
# 删除特定文件名的文件
|
||
def delete_file_with_specific_name(directory, filename='readme', file_format='.md'):
|
||
import os
|
||
for root, dirs, files in os.walk(directory):
|
||
for i0 in range(len(files)):
|
||
if files[i0] == filename+file_format:
|
||
os.remove(root+'/'+files[i0])
|
||
|
||
# 所有文件移到根目录（慎用）
|
||
def move_all_files_to_root_directory(directory):
|
||
import os
|
||
import shutil
|
||
for root, dirs, files in os.walk(directory):
|
||
for i0 in range(len(files)):
|
||
shutil.move(root+'/'+files[i0], directory+'/'+files[i0])
|
||
for i0 in range(100):
|
||
for root, dirs, files in os.walk(directory):
|
||
try:
|
||
os.rmdir(root)
|
||
except:
|
||
pass
|
||
|
||
# 改变当前的目录位置
|
||
def change_directory_by_replacement(current_key_word='code', new_key_word='data'):
|
||
import os
|
||
code_path = os.getcwd()
|
||
data_path = code_path.replace('\\', '/')
|
||
data_path = data_path.replace(current_key_word, new_key_word)
|
||
if os.path.exists(data_path) == False:
|
||
os.makedirs(data_path)
|
||
os.chdir(data_path)
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Module 14: others
|
||
|
||
## download
|
||
|
||
# 通过Sci-Hub网站下载文献
|
||
def download_with_scihub(address=None, num=1):
|
||
from bs4 import BeautifulSoup
|
||
import re
|
||
import requests
|
||
import os
|
||
if num==1 and address!=None:
|
||
address_array = [address]
|
||
else:
|
||
address_array = []
|
||
for i in range(num):
|
||
address = input('\nInput：')
|
||
address_array.append(address)
|
||
for address in address_array:
|
||
r = requests.post('https://sci-hub.st/', data={'request': address})
|
||
print('\nResponse：', r)
|
||
print('Address：', r.url)
|
||
soup = BeautifulSoup(r.text, features='lxml')
|
||
pdf_URL = soup.embed['src']
|
||
# pdf_URL = soup.iframe['src'] # This is a code line of history version which fails to get pdf URL.
|
||
if re.search(re.compile('^https:'), pdf_URL):
|
||
pass
|
||
else:
|
||
pdf_URL = 'https:'+pdf_URL
|
||
print('PDF address：', pdf_URL)
|
||
name = re.search(re.compile('fdp.*?/'),pdf_URL[::-1]).group()[::-1][1::]
|
||
print('PDF name：', name)
|
||
print('Directory：', os.getcwd())
|
||
print('\nDownloading...')
|
||
r = requests.get(pdf_URL, stream=True)
|
||
with open(name, 'wb') as f:
|
||
for chunk in r.iter_content(chunk_size=32):
|
||
f.write(chunk)
|
||
print('Completed!\n')
|
||
if num != 1:
|
||
print('All completed!\n')
|
||
|
||
## PDF
|
||
|
||
# 获取PDF文献中的链接。例如: link_starting_form='https://doi.org'
|
||
def get_links_from_pdf(pdf_path, link_starting_form=''):
|
||
import PyPDF2
|
||
import re
|
||
pdfReader = PyPDF2.PdfFileReader(pdf_path)
|
||
pages = pdfReader.getNumPages()
|
||
i0 = 0
|
||
links = []
|
||
for page in range(pages):
|
||
pageSliced = pdfReader.getPage(page)
|
||
pageObject = pageSliced.getObject()
|
||
if '/Annots' in pageObject.keys():
|
||
ann = pageObject['/Annots']
|
||
old = ''
|
||
for a in ann:
|
||
u = a.getObject()
|
||
if '/A' in u.keys():
|
||
if re.search(re.compile('^'+link_starting_form), u['/A']['/URI']):
|
||
if u['/A']['/URI'] != old:
|
||
links.append(u['/A']['/URI'])
|
||
i0 += 1
|
||
old = u['/A']['/URI']
|
||
return links
|
||
|
||
# 将PDF文件转成文本
|
||
def pdf_to_text(pdf_path):
|
||
from pdfminer.pdfparser import PDFParser, PDFDocument
|
||
from pdfminer.pdfinterp import PDFResourceManager, PDFPageInterpreter
|
||
from pdfminer.converter import PDFPageAggregator
|
||
from pdfminer.layout import LAParams, LTTextBox
|
||
from pdfminer.pdfinterp import PDFTextExtractionNotAllowed
|
||
import logging
|
||
logging.Logger.propagate = False
|
||
logging.getLogger().setLevel(logging.ERROR)
|
||
praser = PDFParser(open(pdf_path, 'rb'))
|
||
doc = PDFDocument()
|
||
praser.set_document(doc)
|
||
doc.set_parser(praser)
|
||
doc.initialize()
|
||
if not doc.is_extractable:
|
||
raise PDFTextExtractionNotAllowed
|
||
else:
|
||
rsrcmgr = PDFResourceManager()
|
||
laparams = LAParams()
|
||
device = PDFPageAggregator(rsrcmgr, laparams=laparams)
|
||
interpreter = PDFPageInterpreter(rsrcmgr, device)
|
||
content = ''
|
||
for page in doc.get_pages():
|
||
interpreter.process_page(page)
|
||
layout = device.get_result()
|
||
for x in layout:
|
||
if isinstance(x, LTTextBox):
|
||
content = content + x.get_text().strip()
|
||
return content
|
||
|
||
|
||
## image
|
||
|
||
# 生成二维码
|
||
def creat_qrcode(data="https://www.guanjihuan.com", filename='a', file_format='.png'):
|
||
import qrcode
|
||
img = qrcode.make(data)
|
||
img.save(filename+file_format)
|
||
|
||
|
||
## audio
|
||
|
||
# 将文本转成音频
|
||
def str_to_audio(str='hello world', filename='str', rate=125, voice=1, read=1, save=0, compress=0, bitrate='16k', print_text=0):
|
||
import pyttsx3
|
||
if print_text==1:
|
||
print(str)
|
||
engine = pyttsx3.init()
|
||
voices = engine.getProperty('voices')
|
||
engine.setProperty('voice', voices[voice].id)
|
||
engine.setProperty("rate", rate)
|
||
if save==1:
|
||
engine.save_to_file(str, filename+'.wav')
|
||
engine.runAndWait()
|
||
print('Wav file saved!')
|
||
if compress==1:
|
||
import os
|
||
os.rename(filename+'.wav', 'temp.wav')
|
||
guan.compress_wav_to_mp3('temp.wav', output_filename=filename+'.mp3', bitrate=bitrate)
|
||
os.remove('temp.wav')
|
||
if read==1:
|
||
engine.say(str)
|
||
engine.runAndWait()
|
||
|
||
# 将txt文件转成音频
|
||
def txt_to_audio(txt_path, rate=125, voice=1, read=1, save=0, compress=0, bitrate='16k', print_text=0):
|
||
import pyttsx3
|
||
f = open(txt_path, 'r', encoding ='utf-8')
|
||
text = f.read()
|
||
if print_text==1:
|
||
print(text)
|
||
engine = pyttsx3.init()
|
||
voices = engine.getProperty('voices')
|
||
engine.setProperty('voice', voices[voice].id)
|
||
engine.setProperty("rate", rate)
|
||
if save==1:
|
||
import re
|
||
filename = re.split('[/,\\\]', txt_path)[-1][:-4]
|
||
engine.save_to_file(text, filename+'.wav')
|
||
engine.runAndWait()
|
||
print('Wav file saved!')
|
||
if compress==1:
|
||
import os
|
||
os.rename(filename+'.wav', 'temp.wav')
|
||
guan.compress_wav_to_mp3('temp.wav', output_filename=filename+'.mp3', bitrate=bitrate)
|
||
os.remove('temp.wav')
|
||
if read==1:
|
||
engine.say(text)
|
||
engine.runAndWait()
|
||
|
||
# 将PDF文件转成音频
|
||
def pdf_to_audio(pdf_path, rate=125, voice=1, read=1, save=0, compress=0, bitrate='16k', print_text=0):
|
||
import pyttsx3
|
||
text = guan.pdf_to_text(pdf_path)
|
||
text = text.replace('\n', ' ')
|
||
if print_text==1:
|
||
print(text)
|
||
engine = pyttsx3.init()
|
||
voices = engine.getProperty('voices')
|
||
engine.setProperty('voice', voices[voice].id)
|
||
engine.setProperty("rate", rate)
|
||
if save==1:
|
||
import re
|
||
filename = re.split('[/,\\\]', pdf_path)[-1][:-4]
|
||
engine.save_to_file(text, filename+'.wav')
|
||
engine.runAndWait()
|
||
print('Wav file saved!')
|
||
if compress==1:
|
||
import os
|
||
os.rename(filename+'.wav', 'temp.wav')
|
||
guan.compress_wav_to_mp3('temp.wav', output_filename=filename+'.mp3', bitrate=bitrate)
|
||
os.remove('temp.wav')
|
||
if read==1:
|
||
engine.say(text)
|
||
engine.runAndWait()
|
||
|
||
# 将wav音频文件压缩成MP3音频文件
|
||
def compress_wav_to_mp3(wav_path, output_filename='a.mp3', bitrate='16k'):
|
||
# Note: Beside the installation of pydub, you may also need download FFmpeg on http://www.ffmpeg.org/download.html and add the bin path to the environment variable.
|
||
from pydub import AudioSegment
|
||
sound = AudioSegment.from_mp3(wav_path)
|
||
sound.export(output_filename,format="mp3",bitrate=bitrate)
|
||
|
||
## words
|
||
|
||
# 播放学术单词
|
||
def play_academic_words(reverse=0, random_on=0, bre_or_ame='ame', show_translation=1, show_link=1, translation_time=2, rest_time=1):
|
||
from bs4 import BeautifulSoup
|
||
import re
|
||
import urllib.request
|
||
import requests
|
||
import os
|
||
import pygame
|
||
import time
|
||
import ssl
|
||
import random
|
||
ssl._create_default_https_context = ssl._create_unverified_context
|
||
html = urllib.request.urlopen("https://www.guanjihuan.com/archives/4418").read().decode('utf-8')
|
||
if bre_or_ame == 'ame':
|
||
directory = 'words_mp3_ameProns/'
|
||
elif bre_or_ame == 'bre':
|
||
directory = 'words_mp3_breProns/'
|
||
exist_directory = os.path.exists(directory)
|
||
html_file = urllib.request.urlopen("https://file.guanjihuan.com/words/"+directory).read().decode('utf-8')
|
||
if exist_directory == 0:
|
||
os.makedirs(directory)
|
||
soup = BeautifulSoup(html, features='lxml')
|
||
contents = re.findall('<h2.*?</a></p>', html, re.S)
|
||
if random_on==1:
|
||
random.shuffle(contents)
|
||
if reverse==1:
|
||
contents.reverse()
|
||
for content in contents:
|
||
soup2 = BeautifulSoup(content, features='lxml')
|
||
all_h2 = soup2.find_all('h2')
|
||
for h2 in all_h2:
|
||
if re.search('\d*. ', h2.get_text()):
|
||
word = re.findall('[a-zA-Z].*', h2.get_text(), re.S)[0]
|
||
exist = os.path.exists(directory+word+'.mp3')
|
||
if not exist:
|
||
try:
|
||
if re.search(word, html_file):
|
||
r = requests.get("https://file.guanjihuan.com/words/"+directory+word+".mp3", stream=True)
|
||
with open(directory+word+'.mp3', 'wb') as f:
|
||
for chunk in r.iter_content(chunk_size=32):
|
||
f.write(chunk)
|
||
except:
|
||
pass
|
||
print(h2.get_text())
|
||
try:
|
||
pygame.mixer.init()
|
||
track = pygame.mixer.music.load(directory+word+'.mp3')
|
||
pygame.mixer.music.play()
|
||
if show_link==1:
|
||
print('https://www.ldoceonline.com/dictionary/'+word)
|
||
except:
|
||
pass
|
||
translation = re.findall('<p>.*?</p>', content, re.S)[0][3:-4]
|
||
if show_translation==1:
|
||
time.sleep(translation_time)
|
||
print(translation)
|
||
time.sleep(rest_time)
|
||
pygame.mixer.music.stop()
|
||
print()
|
||
|
||
# 播放挑选过后的学术单词
|
||
def play_selected_academic_words(reverse=0, random_on=0, bre_or_ame='ame', show_link=1, rest_time=3):
|
||
from bs4 import BeautifulSoup
|
||
import re
|
||
import urllib.request
|
||
import requests
|
||
import os
|
||
import pygame
|
||
import time
|
||
import ssl
|
||
import random
|
||
ssl._create_default_https_context = ssl._create_unverified_context
|
||
html = urllib.request.urlopen("https://www.guanjihuan.com/archives/24732").read().decode('utf-8')
|
||
if bre_or_ame == 'ame':
|
||
directory = 'words_mp3_ameProns/'
|
||
elif bre_or_ame == 'bre':
|
||
directory = 'words_mp3_breProns/'
|
||
exist_directory = os.path.exists(directory)
|
||
html_file = urllib.request.urlopen("https://file.guanjihuan.com/words/"+directory).read().decode('utf-8')
|
||
if exist_directory == 0:
|
||
os.makedirs(directory)
|
||
soup = BeautifulSoup(html, features='lxml')
|
||
contents = re.findall('<li>\d.*?</li>', html, re.S)
|
||
if random_on==1:
|
||
random.shuffle(contents)
|
||
if reverse==1:
|
||
contents.reverse()
|
||
for content in contents:
|
||
soup2 = BeautifulSoup(content, features='lxml')
|
||
all_li = soup2.find_all('li')
|
||
for li in all_li:
|
||
if re.search('\d*. ', li.get_text()):
|
||
word = re.findall('\s[a-zA-Z].*?\s', li.get_text(), re.S)[0][1:-1]
|
||
exist = os.path.exists(directory+word+'.mp3')
|
||
if not exist:
|
||
try:
|
||
if re.search(word, html_file):
|
||
r = requests.get("https://file.guanjihuan.com/words/"+directory+word+".mp3", stream=True)
|
||
with open(directory+word+'.mp3', 'wb') as f:
|
||
for chunk in r.iter_content(chunk_size=32):
|
||
f.write(chunk)
|
||
except:
|
||
pass
|
||
print(li.get_text())
|
||
try:
|
||
pygame.mixer.init()
|
||
track = pygame.mixer.music.load(directory+word+'.mp3')
|
||
pygame.mixer.music.play()
|
||
if show_link==1:
|
||
print('https://www.ldoceonline.com/dictionary/'+word)
|
||
except:
|
||
pass
|
||
time.sleep(rest_time)
|
||
pygame.mixer.music.stop()
|
||
print()
|
||
|
||
# 播放元素周期表上的单词
|
||
def play_element_words(random_on=0, show_translation=1, show_link=1, translation_time=2, rest_time=1):
|
||
from bs4 import BeautifulSoup
|
||
import re
|
||
import urllib.request
|
||
import requests
|
||
import os
|
||
import pygame
|
||
import time
|
||
import ssl
|
||
import random
|
||
ssl._create_default_https_context = ssl._create_unverified_context
|
||
html = urllib.request.urlopen("https://www.guanjihuan.com/archives/10897").read().decode('utf-8')
|
||
directory = 'prons/'
|
||
exist_directory = os.path.exists(directory)
|
||
html_file = urllib.request.urlopen("https://file.guanjihuan.com/words/periodic_table_of_elements/"+directory).read().decode('utf-8')
|
||
if exist_directory == 0:
|
||
os.makedirs(directory)
|
||
soup = BeautifulSoup(html, features='lxml')
|
||
contents = re.findall('<h2.*?</a></p>', html, re.S)
|
||
if random_on==1:
|
||
random.shuffle(contents)
|
||
for content in contents:
|
||
soup2 = BeautifulSoup(content, features='lxml')
|
||
all_h2 = soup2.find_all('h2')
|
||
for h2 in all_h2:
|
||
if re.search('\d*. ', h2.get_text()):
|
||
word = re.findall('[a-zA-Z].* \(', h2.get_text(), re.S)[0][:-2]
|
||
exist = os.path.exists(directory+word+'.mp3')
|
||
if not exist:
|
||
try:
|
||
if re.search(word, html_file):
|
||
r = requests.get("https://file.guanjihuan.com/words/periodic_table_of_elements/prons/"+word+".mp3", stream=True)
|
||
with open(directory+word+'.mp3', 'wb') as f:
|
||
for chunk in r.iter_content(chunk_size=32):
|
||
f.write(chunk)
|
||
except:
|
||
pass
|
||
print(h2.get_text())
|
||
try:
|
||
pygame.mixer.init()
|
||
track = pygame.mixer.music.load(directory+word+'.mp3')
|
||
pygame.mixer.music.play()
|
||
if show_link==1:
|
||
print('https://www.merriam-webster.com/dictionary/'+word)
|
||
except:
|
||
pass
|
||
translation = re.findall('<p>.*?</p>', content, re.S)[0][3:-4]
|
||
if show_translation==1:
|
||
time.sleep(translation_time)
|
||
print(translation)
|
||
time.sleep(rest_time)
|
||
pygame.mixer.music.stop()
|
||
print() |