update

2020.09.30_bandstructure_of_graphene_on_high_symmetric_axes/bandstructure_of_graphene_on_high_symmetric_axes.py

@@ -0,0 +1,77 @@
+"""
+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/6260
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from math import *   # 引入sqrt(), pi, exp等
+import cmath  # 要处理复数情况，用到cmath.exp()
+
+
+def hamiltonian(k1, k2, M=0, t1=1, a=1/sqrt(3)):  # Haldane哈密顿量(a为原子间距，不赋值的话默认为1/sqrt(3)）
+    h0 = np.zeros((2, 2), dtype=complex)
+    h1 = np.zeros((2, 2), dtype=complex)
+    h2 = np.zeros((2, 2), dtype=complex)
+
+    # 质量项(mass term), 用于打开带隙
+    h0[0, 0] = M
+    h0[1, 1] = -M
+
+    # 最近邻项
+    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))
+    h1[0, 1] = h1[1, 0].conj()
+
+    # # 最近邻项也可写成这种形式
+    # 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)
+    # h1[0, 1] = h1[1, 0].conj()
+
+    matrix = h0 + h1
+    return matrix
+
+
+def main():
+    a = 1/sqrt(3)
+    Gamma0 = np.array([0, 0])
+    M0 = np.array([0, 2*pi/3/a])
+    K0 = np.array([2*np.sqrt(3)*pi/9/a, 2*pi/3/a])
+
+    kn = 100  # 每个区域的取点数
+    n = 3  # n个区域（K-Gamma，Gamma-M, M-K）
+    k1_array = np.zeros(kn*n) 
+    k2_array = np.zeros(kn*n)
+
+    # K-Gamma轴
+    k1_array[0:kn] = np.linspace(0, K0[0], kn)[::-1] # [::-1]表示反转数组
+    k2_array[0:kn] = np.linspace(0, K0[1], kn)[::-1]
+
+    # Gamma-M轴
+    k1_array[kn:2*kn] = np.zeros(kn)
+    k2_array[kn:2*kn] = np.linspace(0, M0[1], kn)
+
+    # M-K轴
+    k1_array[2*kn:3*kn] = np.linspace(0, K0[0], kn)
+    k2_array[2*kn:3*kn] = np.ones(kn)*M0[1]
+    
+    i0 = 0
+    dim = hamiltonian(0, 0).shape[0]
+    eigenvalue_k = np.zeros((kn*n, dim))
+    fig, ax = plt.subplots() 
+    for kn0 in range(kn*n):
+        k1 =  k1_array[kn0]
+        k2 =  k2_array[kn0]
+        eigenvalue, eigenvector = np.linalg.eig(hamiltonian(k1, k2))
+        eigenvalue_k[i0, :] = np.sort(np.real(eigenvalue[:]))
+        i0 += 1
+    for dim0 in range(dim):
+        plt.plot(range(kn*n), eigenvalue_k[:, dim0], '-k') 
+    plt.ylabel('E')
+    ax.set_xticks([0, kn, 2*kn, 3*kn])
+    ax.set_xticklabels(['K', 'Gamma', 'M', 'K'])
+    plt.xlim(0, n*kn)
+    plt.grid(axis='x',c='r',linestyle='--')
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()