66 lines
2.0 KiB
Python
66 lines
2.0 KiB
Python
"""
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This code is supported by the website: https://www.guanjihuan.com
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The newest version of this code is on the web page: https://www.guanjihuan.com/archives/408
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from math import *
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import cmath
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import functools
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def hamiltonian(k1, k2, M, t1, a=1/sqrt(3)): # graphene哈密顿量（a为原子间距，不赋值的话默认为1/sqrt(3)）
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# 初始化为零矩阵
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h0 = np.zeros((2, 2), dtype=complex)
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h1 = np.zeros((2, 2), dtype=complex)
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# 质量项(mass term)，用于打开带隙
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h0[0, 0] = M
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h0[1, 1] = -M
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# 最近邻项
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h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a))
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h1[0, 1] = h1[1, 0].conj()
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# # 最近邻项也可写成这种形式
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# h1[1, 0] = t1+t1*cmath.exp(1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)+t1*cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)
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# h1[0, 1] = h1[1, 0].conj()
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matrix = h0 + h1
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return matrix
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def main():
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hamiltonian0 = functools.partial(hamiltonian, M=0, t1=1, a=1/sqrt(3)) # 使用偏函数，固定一些参数
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k1 = np.linspace(-2*pi, 2*pi, 500)
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k2 = np.linspace(-2*pi, 2*pi, 500)
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plot_bands_two_dimension(k1, k2, hamiltonian0)
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def plot_bands_two_dimension(k1, k2, hamiltonian):
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from matplotlib import cm
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dim = hamiltonian(0, 0).shape[0]
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dim1 = k1.shape[0]
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dim2 = k2.shape[0]
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eigenvalue_k = np.zeros((dim2, dim1, dim))
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i0 = 0
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for k10 in k1:
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j0 = 0
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for k20 in k2:
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matrix0 = hamiltonian(k10, k20)
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eigenvalue, eigenvector = np.linalg.eig(matrix0)
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eigenvalue_k[j0, i0, :] = np.sort(np.real(eigenvalue[:]))
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j0 += 1
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i0 += 1
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fig = plt.figure()
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ax = fig.gca(projection='3d')
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k1, k2 = np.meshgrid(k1, k2)
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for dim0 in range(dim):
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ax.plot_surface(k1, k2, eigenvalue_k[:, :, dim0], rcount=200, ccount=200, cmap=cm.coolwarm, linewidth=0, antialiased=False)
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plt.show()
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if __name__ == '__main__':
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main()
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