update

2019.10.23_Hamiltonian_and_bands_of_graphene/1D_graphene.py

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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/408
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from math import *  
+import cmath  
+import functools 
+
+
+def hamiltonian(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
+        h00[i*4+1, i*4+0] = t1
+        h00[i*4+1, i*4+2] = t1
+        h00[i*4+2, i*4+1] = t1
+        h00[i*4+2, i*4+3] = t1
+        h00[i*4+3, i*4+2] = t1
+    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
+        h01[i*4+2, i*4+3] = t1
+
+    matrix = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
+    return matrix
+
+
+def main():
+    hamiltonian0 = functools.partial(hamiltonian, N=40, M=0, t1=1)
+    k = np.linspace(-pi, pi, 300)
+    plot_bands_one_dimension(k, hamiltonian0)
+
+
+def plot_bands_one_dimension(k, hamiltonian):
+    dim = hamiltonian(0).shape[0]
+    dim_k = k.shape[0]
+    eigenvalue_k = np.zeros((dim_k, dim))
+    i0 = 0
+    for k0 in k:
+        matrix0 = hamiltonian(k0)
+        eigenvalue, eigenvector = np.linalg.eig(matrix0)
+        eigenvalue_k[i0, :] = np.sort(np.real(eigenvalue[:]))
+        i0 += 1
+    for dim0 in range(dim):
+        plt.plot(k, eigenvalue_k[:, dim0], '-k')
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()