From 2d125a47ae06ab94da6eddaa3316346e2b2f69e5 Mon Sep 17 00:00:00 2001 From: guanjihuan Date: Sun, 2 Jan 2022 02:58:06 +0800 Subject: [PATCH] Create quantum_transport_in_multi_lead_systems_2.py --- ...antum_transport_in_multi_lead_systems_2.py | 112 ++++++++++++++++++ 1 file changed, 112 insertions(+) create mode 100644 academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems_2.py diff --git a/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems_2.py b/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems_2.py new file mode 100644 index 0000000..fe4e23a --- /dev/null +++ b/academic_codes/2021.02.08_quantum_transport_in_multi_lead_systems/quantum_transport_in_multi_lead_systems_2.py @@ -0,0 +1,112 @@ +""" +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/6075 +""" + +import numpy as np +import time +import guan + +def lead_matrix_00(y): + h00 = np.zeros((y, y)) + for y0 in range(y-1): + h00[y0, y0+1] = 1 + h00[y0+1, y0] = 1 + return h00 + + +def lead_matrix_01(y): + h01 = np.identity(y) + return h01 + + +def scattering_region(x, y): + h = np.zeros((x*y, x*y)) + for x0 in range(x-1): + for y0 in range(y): + h[x0*y+y0, (x0+1)*y+y0] = 1 # x方向的跃迁 + h[(x0+1)*y+y0, x0*y+y0] = 1 + for x0 in range(x): + for y0 in range(y-1): + h[x0*y+y0, x0*y+y0+1] = 1 # y方向的跃迁 + h[x0*y+y0+1, x0*y+y0] = 1 + return h + + +def main(): + start_time = time.time() + width = 5 + length = 50 + fermi_energy_array = np.arange(-4, 4, .01) + + # 中心区的哈密顿量 + H_scattering_region = scattering_region(x=length, y=width) + + # 电极的h00和h01 + lead_h00 = lead_matrix_00(width) + lead_h01 = lead_matrix_01(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) + for i0 in range(width): + h_lead1_to_center[i0, i0] = 1 + h_lead2_to_center[i0, width*i0+(width-1)] = 1 + h_lead3_to_center[i0, width*(length-1-i0)+(width-1)] = 1 + h_lead4_to_center[i0, width*(length-1)+i0] = 1 + h_lead5_to_center[i0, width*(length-1-i0)+0] = 1 + h_lead6_to_center[i0, width*i0+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_scattering_region-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