70 lines
1.8 KiB
Python
70 lines
1.8 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(k, N, M, t1): # graphene哈密顿量（N是条带的宽度参数）
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# 初始化为零矩阵
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h00 = np.zeros((4*N, 4*N), dtype=complex)
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h01 = np.zeros((4*N, 4*N), dtype=complex)
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# 原胞内的跃迁h00
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for i in range(N):
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h00[i*4+0, i*4+0] = M
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h00[i*4+1, i*4+1] = -M
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h00[i*4+2, i*4+2] = M
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h00[i*4+3, i*4+3] = -M
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# 最近邻
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h00[i*4+0, i*4+1] = t1
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h00[i*4+1, i*4+0] = t1
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h00[i*4+1, i*4+2] = t1
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h00[i*4+2, i*4+1] = t1
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h00[i*4+2, i*4+3] = t1
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h00[i*4+3, i*4+2] = t1
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for i in range(N-1):
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# 最近邻
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h00[i*4+3, (i+1)*4+0] = t1
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h00[(i+1)*4+0, i*4+3] = t1
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# 原胞间的跃迁h01
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for i in range(N):
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# 最近邻
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h01[i*4+1, i*4+0] = t1
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h01[i*4+2, i*4+3] = t1
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matrix = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
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return matrix
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def main():
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hamiltonian0 = functools.partial(hamiltonian, N=40, M=0, t1=1)
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k = np.linspace(-pi, pi, 300)
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plot_bands_one_dimension(k, hamiltonian0)
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def plot_bands_one_dimension(k, hamiltonian):
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dim = hamiltonian(0).shape[0]
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dim_k = k.shape[0]
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eigenvalue_k = np.zeros((dim_k, dim))
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i0 = 0
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for k0 in k:
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matrix0 = hamiltonian(k0)
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eigenvalue, eigenvector = np.linalg.eig(matrix0)
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eigenvalue_k[i0, :] = np.sort(np.real(eigenvalue[:]))
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i0 += 1
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for dim0 in range(dim):
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plt.plot(k, eigenvalue_k[:, dim0], '-k')
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plt.show()
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if __name__ == '__main__':
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main()
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