update
This commit is contained in:
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"""
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This code is supported by the website: https://www.guanjihuan.com
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The newest version of this code is on the web page: https://www.guanjihuan.com/archives/6075
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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import copy
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import time
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def get_lead_h00(width):
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h00 = np.zeros((width, width))
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for i0 in range(width-1):
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h00[i0, i0+1] = 1
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h00[i0+1, i0] = 1
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return h00
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def get_lead_h01(width):
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h01 = np.identity(width)
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return h01
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def get_center_hamiltonian(Nx, Ny):
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h = np.zeros((Nx*Ny, Nx*Ny))
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for x0 in range(Nx-1):
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for y0 in range(Ny):
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h[x0*Ny+y0, (x0+1)*Ny+y0] = 1 # x方向的跃迁
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h[(x0+1)*Ny+y0, x0*Ny+y0] = 1
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for x0 in range(Nx):
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for y0 in range(Ny-1):
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h[x0*Ny+y0, x0*Ny+y0+1] = 1 # y方向的跃迁
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h[x0*Ny+y0+1, x0*Ny+y0] = 1
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return h
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def main():
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start_time = time.time()
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width = 5
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length = 50
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fermi_energy_array = np.arange(-4, 4, .01)
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# 中心区的哈密顿量
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H_center = get_center_hamiltonian(Nx=length, Ny=width)
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# 电极的h00和h01
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lead_h00 = get_lead_h00(width)
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lead_h01 = get_lead_h01(width)
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transmission_12_array = []
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transmission_13_array = []
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transmission_14_array = []
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transmission_15_array = []
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transmission_16_array = []
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transmission_1_all_array = []
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for fermi_energy in fermi_energy_array:
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print(fermi_energy)
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# 表面格林函数
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right_lead_surface, left_lead_surface = surface_green_function_lead(fermi_energy + 1e-9j, lead_h00, lead_h01, dim=width)
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# 由于镜面对称以及xy各项同性，因此这里六个电极的表面格林函数具有相同的形式
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lead_1 = copy.deepcopy(right_lead_surface) # 镜面对称使得lead_1=lead_4
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lead_2 = copy.deepcopy(right_lead_surface) # xy各向同性使得lead_2=lead_4
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lead_3 = copy.deepcopy(right_lead_surface)
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lead_4 = copy.deepcopy(right_lead_surface)
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lead_5 = copy.deepcopy(right_lead_surface)
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lead_6 = copy.deepcopy(right_lead_surface)
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# 几何形状如下所示：
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# lead2 lead3
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# lead1(L) lead4(R)
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# lead6 lead5
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# 电极到中心区的跃迁矩阵
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H_lead_1_to_center = np.zeros((width, width*length), dtype=complex)
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H_lead_2_to_center = np.zeros((width, width*length), dtype=complex)
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H_lead_3_to_center = np.zeros((width, width*length), dtype=complex)
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H_lead_4_to_center = np.zeros((width, width*length), dtype=complex)
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H_lead_5_to_center = np.zeros((width, width*length), dtype=complex)
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H_lead_6_to_center = np.zeros((width, width*length), dtype=complex)
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move = 0 # the step of leads 2,3,6,5 moving to center
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for i0 in range(width):
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H_lead_1_to_center[i0, i0] = 1
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H_lead_2_to_center[i0, width*(move+i0)+(width-1)] = 1
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H_lead_3_to_center[i0, width*(length-move-1-i0)+(width-1)] = 1
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H_lead_4_to_center[i0, width*(length-1)+i0] = 1
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H_lead_5_to_center[i0, width*(length-move-1-i0)+0] = 1
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H_lead_6_to_center[i0, width*(move+i0)+0] = 1
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# 自能
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self_energy_1 = np.dot(np.dot(H_lead_1_to_center.transpose().conj(), lead_1), H_lead_1_to_center)
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self_energy_2 = np.dot(np.dot(H_lead_2_to_center.transpose().conj(), lead_2), H_lead_2_to_center)
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self_energy_3 = np.dot(np.dot(H_lead_3_to_center.transpose().conj(), lead_3), H_lead_3_to_center)
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self_energy_4 = np.dot(np.dot(H_lead_4_to_center.transpose().conj(), lead_4), H_lead_4_to_center)
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self_energy_5 = np.dot(np.dot(H_lead_5_to_center.transpose().conj(), lead_5), H_lead_5_to_center)
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self_energy_6 = np.dot(np.dot(H_lead_6_to_center.transpose().conj(), lead_6), H_lead_6_to_center)
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# 整体格林函数
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green = np.linalg.inv(fermi_energy*np.eye(width*length)-H_center-self_energy_1-self_energy_2-self_energy_3-self_energy_4-self_energy_5-self_energy_6)
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# Gamma矩阵
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gamma_1 = 1j*(self_energy_1-self_energy_1.transpose().conj())
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gamma_2 = 1j*(self_energy_2-self_energy_2.transpose().conj())
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gamma_3 = 1j*(self_energy_3-self_energy_3.transpose().conj())
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gamma_4 = 1j*(self_energy_4-self_energy_4.transpose().conj())
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gamma_5 = 1j*(self_energy_5-self_energy_5.transpose().conj())
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gamma_6 = 1j*(self_energy_6-self_energy_6.transpose().conj())
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# Transmission
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transmission_12 = np.trace(np.dot(np.dot(np.dot(gamma_1, green), gamma_2), green.transpose().conj()))
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transmission_13 = np.trace(np.dot(np.dot(np.dot(gamma_1, green), gamma_3), green.transpose().conj()))
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transmission_14 = np.trace(np.dot(np.dot(np.dot(gamma_1, green), gamma_4), green.transpose().conj()))
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transmission_15 = np.trace(np.dot(np.dot(np.dot(gamma_1, green), gamma_5), green.transpose().conj()))
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transmission_16 = np.trace(np.dot(np.dot(np.dot(gamma_1, green), gamma_6), green.transpose().conj()))
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transmission_12_array.append(np.real(transmission_12))
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transmission_13_array.append(np.real(transmission_13))
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transmission_14_array.append(np.real(transmission_14))
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transmission_15_array.append(np.real(transmission_15))
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transmission_16_array.append(np.real(transmission_16))
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transmission_1_all_array.append(np.real(transmission_12+transmission_13+transmission_14+transmission_15+transmission_16))
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Plot_Line(fermi_energy_array, transmission_12_array, xlabel='Fermi energy', ylabel='Transmission_12', title='', filename='a')
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Plot_Line(fermi_energy_array, transmission_13_array, xlabel='Fermi energy', ylabel='Transmission_13', title='', filename='a')
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Plot_Line(fermi_energy_array, transmission_14_array, xlabel='Fermi energy', ylabel='Transmission_14', title='', filename='a')
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Plot_Line(fermi_energy_array, transmission_15_array, xlabel='Fermi energy', ylabel='Transmission_15', title='', filename='a')
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Plot_Line(fermi_energy_array, transmission_16_array, xlabel='Fermi energy', ylabel='Transmission_16', title='', filename='a')
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Plot_Line(fermi_energy_array, transmission_1_all_array, xlabel='Fermi energy', ylabel='Transmission_1_all', title='', filename='a')
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end_time = time.time()
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print('运行时间=', end_time-start_time)
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def Plot_Line(x, y, xlabel='x', ylabel='y', title='', filename='a'):
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import matplotlib.pyplot as plt
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fig, ax = plt.subplots()
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plt.subplots_adjust(bottom=0.20, left=0.18)
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ax.plot(x, y, '-')
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ax.grid()
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ax.set_title(title, fontsize=20, fontfamily='Times New Roman')
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ax.set_xlabel(xlabel, fontsize=20, fontfamily='Times New Roman')
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ax.set_ylabel(ylabel, fontsize=20, fontfamily='Times New Roman')
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ax.tick_params(labelsize=20)
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labels = ax.get_xticklabels() + ax.get_yticklabels()
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[label.set_fontname('Times New Roman') for label in labels]
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# plt.savefig(filename+'.jpg', dpi=300)
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plt.show()
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plt.close('all')
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def transfer_matrix(fermi_energy, h00, h01, dim): # 转移矩阵T
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transfer = np.zeros((2*dim, 2*dim))*(0+0j)
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transfer[0:dim, 0:dim] = np.dot(np.linalg.inv(h01), fermi_energy*np.identity(dim)-h00)
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transfer[0:dim, dim:2*dim] = np.dot(-1*np.linalg.inv(h01), h01.transpose().conj())
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transfer[dim:2*dim, 0:dim] = np.identity(dim)
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transfer[dim:2*dim, dim:2*dim] = 0
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return transfer # 返回转移矩阵
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def surface_green_function_lead(fermi_energy, h00, h01, dim): # 电极的表面格林函数
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transfer = transfer_matrix(fermi_energy, h00, h01, dim)
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eigenvalue, eigenvector = np.linalg.eig(transfer)
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ind = np.argsort(np.abs(eigenvalue))
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temp = np.zeros((2*dim, 2*dim))*(1+0j)
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i0 = 0
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for ind0 in ind:
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temp[:, i0] = eigenvector[:, ind0]
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i0 += 1
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s1 = temp[dim:2*dim, 0:dim]
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s2 = temp[0:dim, 0:dim]
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s3 = temp[dim:2*dim, dim:2*dim]
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s4 = temp[0:dim, dim:2*dim]
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right_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01, s2), np.linalg.inv(s1)))
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left_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), s3), np.linalg.inv(s4)))
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return right_lead_surface, left_lead_surface # 返回右电极的表面格林函数和左电极的表面格林函数
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if __name__ == '__main__':
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main()
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@@ -0,0 +1,87 @@
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"""
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This code is supported by the website: https://www.guanjihuan.com
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The newest version of this code is on the web page: https://www.guanjihuan.com/archives/6075
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"""
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import numpy as np
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import time
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import guan
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def get_lead_h00(width):
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h00 = np.zeros((width, width))
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for i0 in range(width-1):
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h00[i0, i0+1] = 1
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h00[i0+1, i0] = 1
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return h00
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def get_lead_h01(width):
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h01 = np.identity(width)
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return h01
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def get_center_hamiltonian(Nx, Ny):
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h = np.zeros((Nx*Ny, Nx*Ny))
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for x0 in range(Nx-1):
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for y0 in range(Ny):
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h[x0*Ny+y0, (x0+1)*Ny+y0] = 1 # x方向的跃迁
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h[(x0+1)*Ny+y0, x0*Ny+y0] = 1
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for x0 in range(Nx):
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for y0 in range(Ny-1):
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h[x0*Ny+y0, x0*Ny+y0+1] = 1 # y方向的跃迁
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h[x0*Ny+y0+1, x0*Ny+y0] = 1
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return h
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def main():
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start_time = time.time()
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width = 5
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length = 50
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fermi_energy_array = np.arange(-4, 4, .01)
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# 中心区的哈密顿量
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center_hamiltonian = get_center_hamiltonian(Nx=length, Ny=width)
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# 电极的h00和h01
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lead_h00 = get_lead_h00(width)
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lead_h01 = get_lead_h01(width)
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transmission_12_array = []
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transmission_13_array = []
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transmission_14_array = []
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transmission_15_array = []
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transmission_16_array = []
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transmission_1_all_array = []
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for fermi_energy in fermi_energy_array:
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print(fermi_energy)
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# 几何形状如下所示：
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# lead2 lead3
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# lead1(L) lead4(R)
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# lead6 lead5
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transmission_12, transmission_13, transmission_14, transmission_15, transmission_16 = guan.calculate_six_terminal_transmissions_from_lead_1(fermi_energy, h00_for_lead_4=lead_h00, h01_for_lead_4=lead_h01, h00_for_lead_2=lead_h00, h01_for_lead_2=lead_h01, center_hamiltonian=center_hamiltonian, width=width, length=length, internal_degree=1, moving_step_of_leads=0)
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transmission_12_array.append(transmission_12)
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transmission_13_array.append(transmission_13)
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transmission_14_array.append(transmission_14)
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transmission_15_array.append(transmission_15)
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transmission_16_array.append(transmission_16)
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transmission_1_all_array.append(\
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transmission_12+transmission_13+transmission_14+transmission_15+transmission_16)
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# transmission_matrix = guan.calculate_six_terminal_transmission_matrix(fermi_energy, h00_for_lead_4=lead_h00, h01_for_lead_4=lead_h01, h00_for_lead_2=lead_h00, h01_for_lead_2=lead_h01, center_hamiltonian=center_hamiltonian, width=width, length=length, internal_degree=1, moving_step_of_leads=0)
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# transmission_12_array.append(transmission_matrix[0, 1])
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# transmission_13_array.append(transmission_matrix[0, 2])
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# transmission_14_array.append(transmission_matrix[0, 3])
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# transmission_15_array.append(transmission_matrix[0, 4])
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# transmission_16_array.append(transmission_matrix[0, 5])
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# transmission_1_all_array.append(transmission_matrix[0, 1]+transmission_matrix[0, 2]+transmission_matrix[0, 3]+transmission_matrix[0, 4]+transmission_matrix[0, 5])
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guan.plot(fermi_energy_array, transmission_12_array, xlabel='Fermi energy', ylabel='Transmission_12')
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guan.plot(fermi_energy_array, transmission_13_array, xlabel='Fermi energy', ylabel='Transmission_13')
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guan.plot(fermi_energy_array, transmission_14_array, xlabel='Fermi energy', ylabel='Transmission_14')
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guan.plot(fermi_energy_array, transmission_15_array, xlabel='Fermi energy', ylabel='Transmission_15')
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guan.plot(fermi_energy_array, transmission_16_array, xlabel='Fermi energy', ylabel='Transmission_16')
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guan.plot(fermi_energy_array, transmission_1_all_array, xlabel='Fermi energy', ylabel='Transmission_1_all')
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end_time = time.time()
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print('运行时间（分）=', (end_time-start_time)/60)
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if __name__ == '__main__':
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main()
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@@ -0,0 +1,94 @@
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"""
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This code is supported by the website: https://www.guanjihuan.com
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The newest version of this code is on the web page: https://www.guanjihuan.com/archives/6075
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"""
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import kwant
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import numpy as np
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from matplotlib import pyplot
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def make_system():
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a = 1
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lat = kwant.lattice.square(a)
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syst = kwant.Builder()
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t = 1.0
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W = 5
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L = 50
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syst[(lat(x, y) for x in range(L) for y in range(W))] = 0
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syst[lat.neighbors()] = -t
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# 几何形状如下所示：
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# lead2 lead3
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# lead1(L) lead4(R)
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# lead6 lead5
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move = 0 # the step of leads 2,3,6,5 moving to center
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lead1 = kwant.Builder(kwant.TranslationalSymmetry((-a, 0)))
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lead1[(lat(0, j) for j in range(W))] = 0
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lead1[lat.neighbors()] = -t
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syst.attach_lead(lead1)
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lead2 = kwant.Builder(kwant.TranslationalSymmetry((0, -a)))
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lead2[(lat(move+j, 0) for j in range(W))] = 0
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lead2[lat.neighbors()] = -t
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syst.attach_lead(lead2)
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lead3 = kwant.Builder(kwant.TranslationalSymmetry((0, -a)))
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lead3[(lat(j+(L-W-move), 0) for j in range(W))] = 0
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lead3[lat.neighbors()] = -t
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syst.attach_lead(lead3)
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syst.attach_lead(lead1.reversed()) # lead4
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syst.attach_lead(lead3.reversed()) # lead5
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syst.attach_lead(lead2.reversed()) # lead6
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kwant.plot(syst)
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syst = syst.finalized()
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return syst
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def main():
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syst = make_system()
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energies = np.linspace(-4, 4, 800)
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data1 = []
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data2 = []
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data3 = []
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data4 = []
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data5 = []
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data6 = []
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for energy in energies:
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smatrix = kwant.smatrix(syst, energy)
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data1.append(smatrix.transmission(1, 0)) # compute the transmission probability from lead 0 to lead 1
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data2.append(smatrix.transmission(2, 0))
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data3.append(smatrix.transmission(3, 0))
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data4.append(smatrix.transmission(4, 0))
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data5.append(smatrix.transmission(5, 0))
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data6.append(smatrix.transmission(1, 0)+smatrix.transmission(2, 0)+smatrix.transmission(3, 0)+smatrix.transmission(4, 0)+smatrix.transmission(5, 0))
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pyplot.plot(energies, data1)
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pyplot.xlabel("energy [t]")
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pyplot.ylabel("Transmission_12 [e^2/h]")
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pyplot.show()
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pyplot.plot(energies, data2)
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pyplot.xlabel("energy [t]")
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pyplot.ylabel("Transmission_13 [e^2/h]")
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pyplot.show()
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pyplot.plot(energies, data3)
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pyplot.xlabel("energy [t]")
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pyplot.ylabel("Transmission_14 [e^2/h]")
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||||
pyplot.show()
|
||||
pyplot.plot(energies, data4)
|
||||
pyplot.xlabel("energy [t]")
|
||||
pyplot.ylabel("Transmission_15 [e^2/h]")
|
||||
pyplot.show()
|
||||
pyplot.plot(energies, data5)
|
||||
pyplot.xlabel("energy [t]")
|
||||
pyplot.ylabel("Transmission_16 [e^2/h]")
|
||||
pyplot.show()
|
||||
pyplot.plot(energies, data6)
|
||||
pyplot.xlabel("energy [t]")
|
||||
pyplot.ylabel("Transmission_1_all [e^2/h]")
|
||||
pyplot.show()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
main()
|
||||
Reference in New Issue
Block a user