guanjihuan/guanjihuan.com
1
1
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Create Hofstadter_butterfly_of_graphene_ribbon.py

Browse Source
This commit is contained in:
guanjihuan 2021-12-16 19:17:52 +08:00
parent 6865adcbc7
commit 3f7148c3b3
1 changed files with 50 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

50
academic_codes/2021.04.24_Hofstadter_butterfly_of_graphene_ribbon/Hofstadter_butterfly_of_graphene_ribbon.py Normal file
View File

@ -0,0 +1,50 @@
"""
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/12185
"""
import numpy as np
from math import *
import cmath
import functools
import guan
def hamiltonian(B, k, N, M, t1): # graphene哈密顿量（N是条带的宽度参数）
# 初始化为零矩阵
h00 = np.zeros((4*N, 4*N), dtype=complex)
h01 = np.zeros((4*N, 4*N), dtype=complex)
# 原胞内的跃迁h00
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
# 最近邻
h00[i*4+0, i*4+1] = t1*cmath.exp(-2*pi*1j*B*(3*i+1/4)*(np.sqrt(3)/2))
h00[i*4+1, i*4+0] = np.conj(h00[i*4+0, i*4+1])
h00[i*4+1, i*4+2] = t1
h00[i*4+2, i*4+1] = np.conj(h00[i*4+1, i*4+2])
h00[i*4+2, i*4+3] = t1*cmath.exp(2*pi*1j*B*(3*i+7/4)*(np.sqrt(3)/2))
h00[i*4+3, i*4+2] = np.conj(h00[i*4+2, i*4+3])
for i in range(N-1):
# 最近邻
h00[i*4+3, (i+1)*4+0] = t1
h00[(i+1)*4+0, i*4+3] = t1
# 原胞间的跃迁h01
for i in range(N):
# 最近邻
h01[i*4+1, i*4+0] = t1*cmath.exp(-2*pi*1j*B*(3*i+1/4)*(np.sqrt(3)/2))
h01[i*4+2, i*4+3] = t1*cmath.exp(-2*pi*1j*B*(3*i+7/4)*(np.sqrt(3)/2))
matrix = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
return matrix
def main():
N = 30
hamiltonian_function0 = functools.partial(hamiltonian, k=0, N=N, M=0, t1=1)
B_array = np.linspace(0, 1/(3*np.sqrt(3)/2), 100)
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(B_array, hamiltonian_function0)
BS_array = B_array*(3*np.sqrt(3)/2)
guan.plot(BS_array, eigenvalue_array, xlabel='Flux (BS/phi_0)', ylabel='E', title='Ny=%i'%N, filename='a', show=1, save=0, type='k.', y_min=None, y_max=None, markersize=3)
if __name__ == '__main__':
main()