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Update Landau_levels_of_honeycomb_lattice.py

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guanjihuan 2022-08-13 01:53:23 +08:00
parent 8a61baf98e
commit 625ae9918b
1 changed files with 30 additions and 7 deletions
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academic_codes/2022.08.03_Landau_levels_of_honeycomb_lattice/Landau_levels_of_honeycomb_lattice.py
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@ -8,6 +8,7 @@ from math import *
import cmath import cmath
import functools import functools
def hamiltonian(kx, ky, B, N, M, t1, a): # 在磁场下的二维石墨烯，取磁元胞 def hamiltonian(kx, ky, B, N, M, t1, a): # 在磁场下的二维石墨烯，取磁元胞
h00 = np.zeros((4*N, 4*N), dtype=complex) h00 = np.zeros((4*N, 4*N), dtype=complex)
h01 = np.zeros((4*N, 4*N), dtype=complex) h01 = np.zeros((4*N, 4*N), dtype=complex)
@ -38,19 +39,39 @@ def hamiltonian(kx, ky, B, N, M, t1, a): # 在磁场下的二维石墨烯，取
matrix = h00 + h01*cmath.exp(1j*kx) + h01.transpose().conj()*cmath.exp(-1j*kx) matrix = h00 + h01*cmath.exp(1j*kx) + h01.transpose().conj()*cmath.exp(-1j*kx)
return matrix return matrix
def main(): def main():
N = 50 N = 300
a = 1 a = 1
hamiltonian_function = functools.partial(hamiltonian, ky=0, B=1/(3*np.sqrt(3)/2*a*a*N), N=N, M=0, t1=1, a=a) hamiltonian_function = functools.partial(hamiltonian, ky=0, B=1/(3*np.sqrt(3)/2*a*a*N), N=N, M=0, t1=1, a=a)
k_array = np.linspace(-pi, pi, 100)
# 查看能带图
k_array = np.linspace(-pi, pi, 10)
eigenvalue_array = calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function) eigenvalue_array = calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', title='ky=0 N=%i Φ/Φ_0=1/(3*np.sqrt(3)/2*a*a*N)'%N, style='k-') plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', title='ky=0 N=%i Φ/Φ_0=1/(3*np.sqrt(3)/2*a*a*N)'%N, style='k-', y_max=1, y_min=-1)
# import guan # import guan
# k_array = np.linspace(-pi, pi, 10)
# eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function) # eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
# guan.plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', title='ky=0 N=%i Φ/Φ_0=1/(3*np.sqrt(3)/2*a*a*N)'%N, style='k-') # guan.plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', title='ky=0 N=%i Φ/Φ_0=1/(3*np.sqrt(3)/2*a*a*N)'%N, style='k-', y_max=1, y_min=-1)
# 查看关系
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian_function(0))
print('本征值个数：', eigenvalue.shape)
new_eigenvalue = []
for eigen in eigenvalue:
if -0.1<eigen<0.8: # 找某个范围内的本征值
if new_eigenvalue == []:
new_eigenvalue.append(eigen)
else:
if np.abs(eigen-new_eigenvalue[-1])>0.001: # 去除简并
new_eigenvalue.append(eigen)
print('大于等于0的本征值个数：', len(new_eigenvalue), '\n')
print(new_eigenvalue)
plot(range(len(new_eigenvalue)), np.square(np.real(new_eigenvalue)), xlabel='n', ylabel='E^2', style='o-')
def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0): def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0):
dim_x = np.array(x_array).shape[0] dim_x = np.array(x_array).shape[0]
@ -73,6 +94,7 @@ def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print
i0 += 1 i0 += 1
return eigenvalue_array return eigenvalue_array
def plot(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', format='jpg', dpi=300, style='', y_min=None, y_max=None, linewidth=None, markersize=None, adjust_bottom=0.2, adjust_left=0.2): def plot(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', format='jpg', dpi=300, style='', y_min=None, y_max=None, linewidth=None, markersize=None, adjust_bottom=0.2, adjust_left=0.2):
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
fig, ax = plt.subplots() fig, ax = plt.subplots()
@ -97,5 +119,6 @@ def plot(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labels
plt.show() plt.show()
plt.close('all') plt.close('all')
if __name__ == '__main__': if __name__ == '__main__':
main() main()