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Create band_folding.py

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guanjihuan
2022-11-07 00:20:28 +08:00
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commit cfcd1c2ee6
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academic_codes/2022.11.06_band_folding/band_folding.py Normal file
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"""
This code is supported by the website: https://www.guanjihuan.com
The newest version of this code is on the web page: https://www.guanjihuan.com/archives/27656
"""
import guan
import numpy as np
# one dimensional chain model
unit_cell = 0
hopping = 1
hamiltonian_function = guan.one_dimensional_fourier_transform_with_k(unit_cell, hopping)
k_array = np.linspace(-np.pi, np.pi, 100)
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='k', title='one dimensional chain model')
# n times band folding
max_n = 10
for n in np.arange(2, max_n+1):
unit_cell = np.zeros((n, n))
for i0 in range(int(n)):
for j0 in range(int(n)):
if abs(i0-j0)==1:
unit_cell[i0, j0] = 1
hopping = np.zeros((n, n))
hopping[0, n-1] = 1
hamiltonian_function = guan.one_dimensional_fourier_transform_with_k(unit_cell, hopping)
k_array = np.linspace(-np.pi, np.pi, 100)
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='k', title='%i times band folding'%n)