update

2021.12.27_Chern_numbers_of_Landau_levels/Chern_numbers_of_Landau_levels_in_square_lattice.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/18306
+"""
+
+import numpy as np
+from math import *
+import cmath
+import functools
+import guan
+
+def hamiltonian(kx, ky, Ny, B):
+    h00 = np.zeros((Ny, Ny), dtype=complex)
+    h01 = np.zeros((Ny, Ny), dtype=complex)
+    t = 1
+    for iy in range(Ny-1):
+        h00[iy, iy+1] = t
+        h00[iy+1, iy] = t
+    h00[Ny-1, 0] = t*cmath.exp(1j*ky)
+    h00[0, Ny-1] = t*cmath.exp(-1j*ky)
+    for iy in range(Ny):
+        h01[iy, iy] = t*cmath.exp(-2*np.pi*1j*B*iy)
+    matrix = h00 + h01*cmath.exp(1j*kx) + h01.transpose().conj()*cmath.exp(-1j*kx)
+    return matrix
+
+
+def main():
+    Ny = 21
+
+    k_array = np.linspace(-pi, pi, 100)
+    H_k = functools.partial(hamiltonian, ky=0, Ny=Ny, B=1/Ny)
+    eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, H_k)
+    guan.plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', style='k')
+
+    H_k = functools.partial(hamiltonian, Ny=Ny, B=1/Ny)
+    chern_number = guan.calculate_chern_number_for_square_lattice_with_efficient_method(H_k, precision=100)
+    print(chern_number)
+    print(sum(chern_number))
+
+
+if __name__ == '__main__':
+    main()

2021.12.27_Chern_numbers_of_Landau_levels/quantum_transport_of_square_lattice_under_magnetic_fields_in_multi_lead_systems_with_guan.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/18306
+"""
+
+import numpy as np
+import time
+import cmath
+import guan
+
+def get_lead_h00(width):  
+    h00 = np.zeros((width, width))
+    for i0 in range(width-1):
+        h00[i0, i0+1] = 1
+        h00[i0+1, i0] = 1
+    return h00
+
+
+def get_lead_h01(width):
+    h01 = np.identity(width)
+    return h01
+
+
+def get_center_hamiltonian(Nx, Ny, B):
+    h = np.zeros((Nx*Ny, Nx*Ny), dtype=complex)
+    for x0 in range(Nx-1):
+        for y0 in range(Ny):
+            h[x0*Ny+y0, (x0+1)*Ny+y0] = 1*cmath.exp(-2*np.pi*1j*B*y0) # x方向的跃迁
+            h[(x0+1)*Ny+y0, x0*Ny+y0] = 1*cmath.exp(2*np.pi*1j*B*y0)
+    for x0 in range(Nx):
+        for y0 in range(Ny-1):
+            h[x0*Ny+y0, x0*Ny+y0+1] = 1 # y方向的跃迁
+            h[x0*Ny+y0+1, x0*Ny+y0] = 1 
+    return h
+
+
+def main():
+    start_time = time.time()
+    width = 21
+    length = 72
+    fermi_energy_array = np.arange(-4, 4, .05)
+
+    # 中心区的哈密顿量
+    H_cetner = get_center_hamiltonian(Nx=length, Ny=width, B=1/width)
+
+    # 电极的h00和h01
+    lead_h00 = get_lead_h00(width)
+    lead_h01 = get_lead_h01(width)
+    
+    transmission_12_array = []
+    transmission_13_array = []
+    transmission_14_array = []
+    transmission_15_array = []
+    transmission_16_array = []
+    transmission_1_all_array = []
+
+    for fermi_energy in fermi_energy_array:
+        print(fermi_energy)
+        #   几何形状如下所示：
+        #               lead2         lead3
+        #   lead1(L)                          lead4(R)  
+        #               lead6         lead5 
+
+        # 电极到中心区的跃迁矩阵
+        h_lead1_to_center = np.zeros((width, width*length), dtype=complex)
+        h_lead2_to_center = np.zeros((width, width*length), dtype=complex)
+        h_lead3_to_center = np.zeros((width, width*length), dtype=complex)
+        h_lead4_to_center = np.zeros((width, width*length), dtype=complex)
+        h_lead5_to_center = np.zeros((width, width*length), dtype=complex)
+        h_lead6_to_center = np.zeros((width, width*length), dtype=complex)
+        move = 10 # the step of leads 2,3,6,5 moving to center
+        for i0 in range(width):
+            h_lead1_to_center[i0, i0] = 1
+            h_lead2_to_center[i0, width*(move+i0)+(width-1)] = 1
+            h_lead3_to_center[i0, width*(length-move-1-i0)+(width-1)] = 1
+            h_lead4_to_center[i0, width*(length-1)+i0] = 1
+            h_lead5_to_center[i0, width*(length-move-1-i0)+0] = 1
+            h_lead6_to_center[i0, width*(i0+move)+0] = 1
+        # 自能    
+        self_energy1, gamma1 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, lead_h00, lead_h01, h_lead1_to_center)
+        self_energy2, gamma2 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, lead_h00, lead_h01, h_lead2_to_center)
+        self_energy3, gamma3 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, lead_h00, lead_h01, h_lead3_to_center)
+        self_energy4, gamma4 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, lead_h00, lead_h01, h_lead4_to_center)
+        self_energy5, gamma5 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, lead_h00, lead_h01, h_lead5_to_center)
+        self_energy6, gamma6 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, lead_h00, lead_h01, h_lead6_to_center)
+
+        # 整体格林函数
+        green = np.linalg.inv(fermi_energy*np.eye(width*length)-H_cetner-self_energy1-self_energy2-self_energy3-self_energy4-self_energy5-self_energy6)
+
+        # Transmission
+        transmission_12 = np.trace(np.dot(np.dot(np.dot(gamma1, green), gamma2), green.transpose().conj()))
+        transmission_13 = np.trace(np.dot(np.dot(np.dot(gamma1, green), gamma3), green.transpose().conj()))
+        transmission_14 = np.trace(np.dot(np.dot(np.dot(gamma1, green), gamma4), green.transpose().conj()))
+        transmission_15 = np.trace(np.dot(np.dot(np.dot(gamma1, green), gamma5), green.transpose().conj()))
+        transmission_16 = np.trace(np.dot(np.dot(np.dot(gamma1, green), gamma6), green.transpose().conj()))
+        transmission_12_array.append(np.real(transmission_12))
+        transmission_13_array.append(np.real(transmission_13))
+        transmission_14_array.append(np.real(transmission_14))
+        transmission_15_array.append(np.real(transmission_15))
+        transmission_16_array.append(np.real(transmission_16))
+        transmission_1_all_array.append(np.real(transmission_12+transmission_13+transmission_14+transmission_15+transmission_16))
+    
+    guan.plot(fermi_energy_array, transmission_12_array, xlabel='Fermi energy', ylabel='Transmission_12')
+    guan.plot(fermi_energy_array, transmission_13_array, xlabel='Fermi energy', ylabel='Transmission_13')
+    guan.plot(fermi_energy_array, transmission_14_array, xlabel='Fermi energy', ylabel='Transmission_14')
+    guan.plot(fermi_energy_array, transmission_15_array, xlabel='Fermi energy', ylabel='Transmission_15')
+    guan.plot(fermi_energy_array, transmission_16_array, xlabel='Fermi energy', ylabel='Transmission_16')
+    guan.plot(fermi_energy_array, transmission_1_all_array, xlabel='Fermi energy', ylabel='Transmission_1_all')
+    end_time = time.time()
+    print('运行时间=', end_time-start_time)
+
+
+if __name__ == '__main__':
+    main()