update

2020.01.03_calculation_of_local_currents/calculation_of_local_currents.py

@@ -0,0 +1,129 @@
+"""
+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/3888
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+import time
+
+
+def matrix_00(width=10):  # 电极元胞内跃迁，width不赋值时默认为10  
+    h00 = np.zeros((width, width))
+    for width0 in range(width-1):
+        h00[width0, width0+1] = 1
+        h00[width0+1, width0] = 1
+    return h00
+
+
+def matrix_01(width=10):  # 电极元胞间跃迁，width不赋值时默认为10
+    h01 = np.identity(width)
+    return h01
+
+
+def matrix_LC(width=10, length=300):  # 左电极跳到中心区
+    h_LC = np.zeros((width, width*length))
+    for width0 in range(width):
+        h_LC[width0, width0] = 1
+    return h_LC
+
+
+def matrix_CR(width=10, length=300):  # 中心区跳到右电极
+    h_CR = np.zeros((width*length, width))
+    for width0 in range(width):
+        h_CR[width*(length-1)+width0, width0] = 1
+    return h_CR
+
+
+def matrix_center(width=10, length=300):  # 中心区哈密顿量
+    hamiltonian = np.zeros((width*length, width*length))
+    for length0 in range(length-1):
+        for width0 in range(width):
+            hamiltonian[width*length0+width0, width*(length0+1)+width0] = 1  # 长度方向跃迁
+            hamiltonian[width*(length0+1)+width0, width*length0+width0] = 1 
+    for length0 in range(length):
+        for width0 in range(width-1):
+            hamiltonian[width*length0+width0, width*length0+width0+1] = 1  # 宽度方向跃迁
+            hamiltonian[width*length0+width0+1, width*length0+width0] = 1
+    # 中间加势垒
+    for j0 in range(6):
+        for i0 in range(6): 
+            hamiltonian[width*(int(length/2)-3+j0)+int(width/2)-3+i0, width*(int(length/2)-3+j0)+int(width/2)-3+i0]= 1e8
+    return hamiltonian
+
+
+def main():
+    start_time = time.time()
+    fermi_energy = 0
+    width = 60
+    length = 100
+    h00 = matrix_00(width)
+    h01 = matrix_01(width)
+    G_n = Green_n(fermi_energy+1j*1e-9, h00, h01, width, length)
+    # 下面是提取数据并画图
+    direction_x = np.zeros((width, length))
+    direction_y = np.zeros((width, length))
+    for length0 in range(length-1):
+        for width0 in range(width):
+            direction_x[width0, length0] = G_n[width*length0+width0, width*(length0+1)+width0]
+    for length0 in range(length):
+        for width0 in range(width-1):
+            direction_y[width0, length0] = G_n[width*length0+width0, width*length0+width0+1]
+    # print(direction_x)
+    # print(direction_y)
+    X, Y = np.meshgrid(range(length), range(width))
+    plt.quiver(X, Y, direction_x, direction_y)
+    plt.show()
+    end_time = time.time()
+    print('运行时间=', end_time-start_time)
+
+
+
+def transfer_matrix(fermi_energy, h00, h01, dim):   # 转移矩阵T。dim是传递矩阵h00和h01的维度
+    transfer = np.zeros((2*dim, 2*dim), dtype=complex)
+    transfer[0:dim, 0:dim] = np.dot(np.linalg.inv(h01), fermi_energy*np.identity(dim)-h00)   # np.dot()等效于np.matmul()
+    transfer[0:dim, dim:2*dim] = np.dot(-1*np.linalg.inv(h01), h01.transpose().conj())
+    transfer[dim:2*dim, 0:dim] = np.identity(dim)
+    transfer[dim:2*dim, dim:2*dim] = 0  # a:b代表 a <= x < b
+    return transfer  # 返回转移矩阵
+
+
+def green_function_lead(fermi_energy, h00, h01, dim):  # 电极的表面格林函数
+    transfer = transfer_matrix(fermi_energy, h00, h01, dim)
+    eigenvalue, eigenvector = np.linalg.eig(transfer)
+    ind = np.argsort(np.abs(eigenvalue))
+    temp = np.zeros((2*dim, 2*dim))*(1+0j)
+    i0 = 0
+    for ind0 in ind:
+        temp[:, i0] = eigenvector[:, ind0]
+        i0 += 1
+    s1 = temp[dim:2*dim, 0:dim]
+    s2 = temp[0:dim, 0:dim]
+    s3 = temp[dim:2*dim, dim:2*dim]
+    s4 = temp[0:dim, dim:2*dim]
+    right_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01, s2), np.linalg.inv(s1)))
+    left_lead_surface = np.linalg.inv(fermi_energy*np.identity(dim)-h00-np.dot(np.dot(h01.transpose().conj(), s3), np.linalg.inv(s4)))
+    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
+
+
+def self_energy_lead(fermi_energy, h00, h01, width, length):  # 电极的自能
+    h_LC = matrix_LC(width, length)
+    h_CR = matrix_CR(width, length)
+    right_lead_surface, left_lead_surface = green_function_lead(fermi_energy, h00, h01, width)
+    right_self_energy = np.dot(np.dot(h_CR, right_lead_surface), h_CR.transpose().conj())
+    left_self_energy = np.dot(np.dot(h_LC.transpose().conj(), left_lead_surface), h_LC)
+    return right_self_energy, left_self_energy  # 返回右电极的自能和左电极的自能
+
+
+def Green_n(fermi_energy, h00, h01, width, length):  # 计算G_n
+    right_self_energy, left_self_energy = self_energy_lead(fermi_energy, h00, h01, width, length)
+    hamiltonian = matrix_center(width, length)
+    green = np.linalg.inv(fermi_energy*np.identity(width*length)-hamiltonian-left_self_energy-right_self_energy)
+    right_self_energy = (right_self_energy - right_self_energy.transpose().conj())*1j
+    left_self_energy = (left_self_energy - left_self_energy.transpose().conj())*1j
+    G_n = np.imag(np.dot(np.dot(green, left_self_energy), green.transpose().conj()))
+    return G_n
+
+
+if __name__ == '__main__':
+    main()

2020.01.03_calculation_of_local_currents/calculation_of_local_currents_with_Kwant.py

@@ -0,0 +1,46 @@
+"""
+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/3888
+"""
+
+import kwant
+
+
+def make_system():
+    a = 1
+    lat = kwant.lattice.square(a, norbs=1)  # 创建晶格，方格子
+    syst = kwant.Builder() 
+    t = 1.0
+    W = 60  # 中心体系宽度
+    L = 100  # 中心体系长度
+    # 给中心体系赋值
+    for i in range(L):
+        for j in range(W):
+            syst[lat(i, j)] = 0
+            if j > 0:
+                syst[lat(i, j), lat(i, j-1)] = -t  # hopping in y-direction
+            if i > 0:
+                syst[lat(i, j), lat(i-1, j)] = -t  # hopping in x-direction
+            if 47<=i<53 and 27<=j<33:  # 势垒
+                syst[lat(i, j)] = 1e8
+    # 电极
+    lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0)))
+    lead[(lat(0, j) for j in range(W))] = 0
+    lead[lat.neighbors()] = -t  # 用neighbors()方法
+    syst.attach_lead(lead)  # 左电极
+    syst.attach_lead(lead.reversed())   # 用reversed()方法得到右电极
+    # 制作结束
+    kwant.plot(syst) 
+    syst = syst.finalized()  
+    return syst
+
+
+def main():
+    syst = make_system()
+    psi = kwant.wave_function(syst)(0)[29]
+    current = kwant.operator.Current(syst)(psi)
+    kwant.plotter.current(syst, current)
+
+
+if __name__ == '__main__':
+    main()

2020.01.03_calculation_of_local_currents/calculation_of_local_currents_with_guan.py

@@ -0,0 +1,85 @@
+"""
+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/3888
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+import time
+import guan
+
+def matrix_00(width=10):  # 电极元胞内跃迁，width不赋值时默认为10  
+    h00 = np.zeros((width, width))
+    for width0 in range(width-1):
+        h00[width0, width0+1] = 1
+        h00[width0+1, width0] = 1
+    return h00
+
+
+def matrix_01(width=10):  # 电极元胞间跃迁，width不赋值时默认为10
+    h01 = np.identity(width)
+    return h01
+
+
+def matrix_LC(width=10, length=300):  # 左电极跳到中心区
+    h_LC = np.zeros((width, width*length))
+    for width0 in range(width):
+        h_LC[width0, width0] = 1
+    return h_LC
+
+
+def matrix_CR(width=10, length=300):  # 中心区跳到右电极
+    h_CR = np.zeros((width*length, width))
+    for width0 in range(width):
+        h_CR[width*(length-1)+width0, width0] = 1
+    return h_CR
+
+
+def matrix_center(width=10, length=300):  # 中心区哈密顿量
+    hamiltonian = np.zeros((width*length, width*length))
+    for length0 in range(length-1):
+        for width0 in range(width):
+            hamiltonian[width*length0+width0, width*(length0+1)+width0] = 1  # 长度方向跃迁
+            hamiltonian[width*(length0+1)+width0, width*length0+width0] = 1 
+    for length0 in range(length):
+        for width0 in range(width-1):
+            hamiltonian[width*length0+width0, width*length0+width0+1] = 1  # 宽度方向跃迁
+            hamiltonian[width*length0+width0+1, width*length0+width0] = 1
+    # 中间加势垒
+    for j0 in range(6):
+        for i0 in range(6): 
+            hamiltonian[width*(int(length/2)-3+j0)+int(width/2)-3+i0, width*(int(length/2)-3+j0)+int(width/2)-3+i0]= 1e8
+    return hamiltonian
+
+
+def main():
+    start_time = time.time()
+    fermi_energy = 0
+    width = 60
+    length = 100
+    h00 = matrix_00(width)
+    h01 = matrix_01(width)
+    h_LC = matrix_LC(width, length)
+    h_CR = matrix_CR(width, length)
+    hamiltonian = matrix_center(width, length) 
+    
+    G_n = guan.electron_correlation_function_green_n_for_local_current(fermi_energy, h00, h01, h_LC, h_CR, hamiltonian)
+
+    direction_x = np.zeros((width, length))
+    direction_y = np.zeros((width, length))
+    for length0 in range(length-1):
+        for width0 in range(width):
+            direction_x[width0, length0] = G_n[width*length0+width0, width*(length0+1)+width0]
+    for length0 in range(length):
+        for width0 in range(width-1):
+            direction_y[width0, length0] = G_n[width*length0+width0, width*length0+width0+1]
+
+    X, Y = np.meshgrid(range(length), range(width))
+    plt.quiver(X, Y, direction_x, direction_y)
+    plt.show()
+    end_time = time.time()
+    print('运行时间=', end_time-start_time)
+
+
+if __name__ == '__main__':
+    main()