Create Landau_levels_of_honeycomb_lattice.py

academic_codes/2022.08.03_Landau_levels_of_honeycomb_lattice/Landau_levels_of_honeycomb_lattice.py

@@ -0,0 +1,101 @@
+"""
+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/23834
+"""
+
+import numpy as np
+from math import *  
+import cmath  
+import functools 
+
+def hamiltonian(kx, ky, B, N, M, t1, a):  # 在磁场下的二维石墨烯，取磁元胞
+    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*a*i+1/4*a)*(np.sqrt(3)/2*a))
+        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*a*i+7/4*a)*(np.sqrt(3)/2)*a)
+        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
+    h00[4*(N-1)+3, 0] = t1*cmath.exp(1j*ky)
+    h00[0, 4*(N-1)+3] = t1*cmath.exp(-1j*ky)
+    # 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*a*i+1/4*a)*(np.sqrt(3)/2*a))
+        h01[i*4+2, i*4+3] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+7/4*a)*(np.sqrt(3)/2*a))
+    matrix = h00 + h01*cmath.exp(1j*kx) + h01.transpose().conj()*cmath.exp(-1j*kx)
+    return matrix
+
+def main():
+    N = 50
+    a = 1
+
+    hamiltonian_function = functools.partial(hamiltonian, ky=0, B=1/(3*np.sqrt(3)/2*a*a*N), N=N, M=0, t1=1, a=a)
+    k_array = np.linspace(-pi, pi, 100)
+    
+    eigenvalue_array = calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
+    plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', title='ky=0    N=%i    Φ/Φ_0=1/(3*np.sqrt(3)/2*a*a*N)'%N, style='k-')
+
+    # import guan
+    # eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
+    # guan.plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', title='ky=0    N=%i    Φ/Φ_0=1/(3*np.sqrt(3)/2*a*a*N)'%N, style='k-')
+
+def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0):
+    dim_x = np.array(x_array).shape[0]
+    i0 = 0
+    if np.array(hamiltonian_function(0)).shape==():
+        eigenvalue_array = np.zeros((dim_x, 1))
+        for x0 in x_array:
+            hamiltonian = hamiltonian_function(x0)
+            eigenvalue_array[i0, 0] = np.real(hamiltonian)
+            i0 += 1
+    else:
+        dim = np.array(hamiltonian_function(0)).shape[0]
+        eigenvalue_array = np.zeros((dim_x, dim))
+        for x0 in x_array:
+            if print_show==1:
+                print(x0)
+            hamiltonian = hamiltonian_function(x0)
+            eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
+            eigenvalue_array[i0, :] = eigenvalue
+            i0 += 1
+    return eigenvalue_array
+
+def plot(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', format='jpg', dpi=300, style='', y_min=None, y_max=None, linewidth=None, markersize=None, adjust_bottom=0.2, adjust_left=0.2): 
+    import matplotlib.pyplot as plt
+    fig, ax = plt.subplots()
+    plt.subplots_adjust(bottom=adjust_bottom, left=adjust_left)
+    ax.grid()
+    ax.tick_params(labelsize=labelsize) 
+    labels = ax.get_xticklabels() + ax.get_yticklabels()
+    [label.set_fontname('Times New Roman') for label in labels]
+    ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize)
+    ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
+    ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman') 
+    ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman') 
+    if y_min!=None or y_max!=None:
+        if y_min==None:
+            y_min=min(y_array)
+        if y_max==None:
+            y_max=max(y_array)
+        ax.set_ylim(y_min, y_max)
+    if save == 1:
+        plt.savefig(filename+'.'+format, dpi=dpi) 
+    if show == 1:
+        plt.show()
+    plt.close('all')
+
+if __name__ == '__main__':
+    main()