From 444daabd6e8500be95274fc378d019ac3dbf76d0 Mon Sep 17 00:00:00 2001 From: guanjihuan Date: Mon, 10 Jan 2022 15:49:36 +0800 Subject: [PATCH] Create quantum_transport_of_square_lattice_under_magnetic_fields_in_multi_lead_systems_with_guan.py --- ..._fields_in_multi_lead_systems_with_guan.py | 114 ++++++++++++++++++ 1 file changed, 114 insertions(+) create mode 100644 academic_codes/2021.12.27_Chern_numbers_of_Landau_levels/quantum_transport_of_square_lattice_under_magnetic_fields_in_multi_lead_systems_with_guan.py diff --git a/academic_codes/2021.12.27_Chern_numbers_of_Landau_levels/quantum_transport_of_square_lattice_under_magnetic_fields_in_multi_lead_systems_with_guan.py b/academic_codes/2021.12.27_Chern_numbers_of_Landau_levels/quantum_transport_of_square_lattice_under_magnetic_fields_in_multi_lead_systems_with_guan.py new file mode 100644 index 0000000..164ca3f --- /dev/null +++ b/academic_codes/2021.12.27_Chern_numbers_of_Landau_levels/quantum_transport_of_square_lattice_under_magnetic_fields_in_multi_lead_systems_with_guan.py @@ -0,0 +1,114 @@ +""" +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 = 30 + length = 80 + fermi_energy_array = np.arange(-4, 4, .02) + + # 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 + 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() \ No newline at end of file