599 lines
40 KiB
Python
599 lines
40 KiB
Python
# Module: quantum_transport
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# 计算电导
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def calculate_conductance(fermi_energy, h00, h01, length=100):
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import numpy as np
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import copy
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import guan
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right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
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for ix in range(length):
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if ix == 0:
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green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
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green_0n_n = copy.deepcopy(green_nn_n)
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elif ix != length-1:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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else:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
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return conductance
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# 计算不同费米能下的电导
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def calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01, length=100, print_show=0):
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import numpy as np
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import guan
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dim = np.array(fermi_energy_array).shape[0]
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conductance_array = np.zeros(dim)
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i0 = 0
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for fermi_energy in fermi_energy_array:
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conductance_array[i0] = np.real(guan.calculate_conductance(fermi_energy, h00, h01, length))
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if print_show == 1:
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print(fermi_energy, conductance_array[i0])
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i0 += 1
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return conductance_array
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# 计算在势垒散射下的电导
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def calculate_conductance_with_barrier(fermi_energy, h00, h01, length=100, barrier_length=20, barrier_potential=1):
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import numpy as np
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import copy
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import guan
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right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
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dim = np.array(h00).shape[0]
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for ix in range(length):
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if ix == 0:
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green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
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green_0n_n = copy.deepcopy(green_nn_n)
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elif int(length/2-barrier_length/2)<=ix<int(length/2+barrier_length/2):
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00+barrier_potential*np.identity(dim), h01, green_nn_n, broadening=0)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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elif ix != length-1:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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else:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
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return conductance
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# 计算在无序散射下的电导
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def calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100, calculation_times=1):
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import numpy as np
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import copy
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import guan
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right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
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dim = np.array(h00).shape[0]
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conductance_averaged = 0
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for times in range(calculation_times):
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for ix in range(length+2):
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disorder = np.zeros((dim, dim))
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for dim0 in range(dim):
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if np.random.uniform(0, 1)<=disorder_concentration:
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disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
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if ix == 0:
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green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
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green_0n_n = copy.deepcopy(green_nn_n)
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elif ix != length+1:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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else:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
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conductance_averaged += conductance
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conductance_averaged = conductance_averaged/calculation_times
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return conductance_averaged
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# 计算在无序散射下的电导（需要输入无序数组）
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def calculate_conductance_with_disorder_array(fermi_energy, h00, h01, disorder_array, length=100):
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import numpy as np
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import copy
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import guan
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right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
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dim = np.array(h00).shape[0]
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i0 = 0
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for ix in range(length+2):
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if ix == 0:
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green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
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green_0n_n = copy.deepcopy(green_nn_n)
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elif ix != length+1:
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disorder = np.diag(disorder_array[i0*dim:(i0+1)*dim])
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i0 += 1
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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else:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
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return conductance
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# 计算在无序垂直切片的散射下的电导
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def calculate_conductance_with_slice_disorder(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100):
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import numpy as np
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import copy
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import guan
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right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
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dim = np.array(h00).shape[0]
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for ix in range(length+2):
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disorder = np.zeros((dim, dim))
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if np.random.uniform(0, 1)<=disorder_concentration:
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disorder = np.random.uniform(-disorder_intensity, disorder_intensity)*np.eye(dim)
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if ix == 0:
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green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
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green_0n_n = copy.deepcopy(green_nn_n)
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elif ix != length+1:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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else:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
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return conductance
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# 计算在无序水平切片的散射下的电导
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def calculate_conductance_with_disorder_inside_unit_cell_which_keeps_translational_symmetry(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100):
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import numpy as np
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import copy
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import guan
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right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
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dim = np.array(h00).shape[0]
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disorder = np.zeros((dim, dim))
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for dim0 in range(dim):
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if np.random.uniform(0, 1)<=disorder_concentration:
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disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
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for ix in range(length+2):
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if ix == 0:
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green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
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green_0n_n = copy.deepcopy(green_nn_n)
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elif ix != length+1:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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else:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
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return conductance
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# 计算在随机空位的散射下的电导
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def calculate_conductance_with_random_vacancy(fermi_energy, h00, h01, vacancy_concentration=0.5, vacancy_potential=1e9, length=100):
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import numpy as np
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import copy
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import guan
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right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01)
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dim = np.array(h00).shape[0]
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for ix in range(length+2):
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random_vacancy = np.zeros((dim, dim))
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for dim0 in range(dim):
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if np.random.uniform(0, 1)<=vacancy_concentration:
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random_vacancy[dim0, dim0] = vacancy_potential
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if ix == 0:
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green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
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green_0n_n = copy.deepcopy(green_nn_n)
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elif ix != length+1:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00+random_vacancy, h01, green_nn_n, broadening=0)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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else:
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green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
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green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
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conductance = np.trace(np.dot(np.dot(np.dot(gamma_left, green_0n_n), gamma_right), green_0n_n.transpose().conj()))
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return conductance
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# 计算在不同无序散射强度下的电导
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def calculate_conductance_with_disorder_intensity_array(fermi_energy, h00, h01, disorder_intensity_array, disorder_concentration=1.0, length=100, calculation_times=1, print_show=0):
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import numpy as np
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import guan
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dim = np.array(disorder_intensity_array).shape[0]
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conductance_array = np.zeros(dim)
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i0 = 0
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for disorder_intensity in disorder_intensity_array:
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for times in range(calculation_times):
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conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
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if print_show == 1:
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print(disorder_intensity, conductance_array[i0]/calculation_times)
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i0 += 1
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conductance_array = conductance_array/calculation_times
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return conductance_array
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# 计算在不同无序浓度下的电导
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def calculate_conductance_with_disorder_concentration_array(fermi_energy, h00, h01, disorder_concentration_array, disorder_intensity=2.0, length=100, calculation_times=1, print_show=0):
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import numpy as np
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import guan
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dim = np.array(disorder_concentration_array).shape[0]
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conductance_array = np.zeros(dim)
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i0 = 0
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for disorder_concentration in disorder_concentration_array:
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for times in range(calculation_times):
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conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
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if print_show == 1:
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print(disorder_concentration, conductance_array[i0]/calculation_times)
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i0 += 1
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conductance_array = conductance_array/calculation_times
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return conductance_array
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# 计算在不同无序散射长度下的电导
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def calculate_conductance_with_scattering_length_array(fermi_energy, h00, h01, length_array, disorder_intensity=2.0, disorder_concentration=1.0, calculation_times=1, print_show=0):
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import numpy as np
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import guan
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dim = np.array(length_array).shape[0]
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conductance_array = np.zeros(dim)
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i0 = 0
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for length in length_array:
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for times in range(calculation_times):
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conductance_array[i0] = conductance_array[i0]+np.real(guan.calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=disorder_intensity, disorder_concentration=disorder_concentration, length=length))
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if print_show == 1:
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print(length, conductance_array[i0]/calculation_times)
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i0 += 1
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conductance_array = conductance_array/calculation_times
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return conductance_array
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# 计算得到Gamma矩阵和格林函数，用于计算六端口的量子输运
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def get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
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import numpy as np
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import guan
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# ---------------- Geometry ----------------
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# lead2 lead3
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# lead1(L) lead4(R)
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# lead6 lead5
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h00_for_lead_1 = h00_for_lead_4
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h00_for_lead_2 = h00_for_lead_2
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h00_for_lead_3 = h00_for_lead_2
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h00_for_lead_5 = h00_for_lead_2
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h00_for_lead_6 = h00_for_lead_2
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h00_for_lead_4 = h00_for_lead_4
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h01_for_lead_1 = h01_for_lead_4.transpose().conj()
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h01_for_lead_2 = h01_for_lead_2
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h01_for_lead_3 = h01_for_lead_2
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h01_for_lead_4 = h01_for_lead_4
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h01_for_lead_5 = h01_for_lead_2.transpose().conj()
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h01_for_lead_6 = h01_for_lead_2.transpose().conj()
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h_lead1_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
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h_lead2_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
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h_lead3_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
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h_lead4_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
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h_lead5_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
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h_lead6_to_center = np.zeros((internal_degree*width, internal_degree*width*length), dtype=complex)
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move = moving_step_of_leads # the step of leads 2,3,6,5 moving to center
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h_lead1_to_center[0:internal_degree*width, 0:internal_degree*width] = h01_for_lead_1.transpose().conj()
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h_lead4_to_center[0:internal_degree*width, internal_degree*width*(length-1):internal_degree*width*length] = h01_for_lead_4.transpose().conj()
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for i0 in range(width):
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begin_index = internal_degree*i0+0
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end_index = internal_degree*i0+internal_degree
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h_lead2_to_center[begin_index:end_index, internal_degree*(width*(move+i0)+(width-1))+0:internal_degree*(width*(move+i0)+(width-1))+internal_degree] = h01_for_lead_2.transpose().conj()[begin_index:end_index, begin_index:end_index]
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h_lead3_to_center[begin_index:end_index, internal_degree*(width*(length-move-1-i0)+(width-1))+0:internal_degree*(width*(length-move-1-i0)+(width-1))+internal_degree] = h01_for_lead_3.transpose().conj()[begin_index:end_index, begin_index:end_index]
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h_lead5_to_center[begin_index:end_index, internal_degree*(width*(length-move-1-i0)+0)+0:internal_degree*(width*(length-move-1-i0)+0)+internal_degree] = h01_for_lead_5.transpose().conj()[begin_index:end_index, begin_index:end_index]
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h_lead6_to_center[begin_index:end_index, internal_degree*(width*(i0+move)+0)+0:internal_degree*(width*(i0+move)+0)+internal_degree] = h01_for_lead_6.transpose().conj()[begin_index:end_index, begin_index:end_index]
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self_energy1, gamma1 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_1, h01_for_lead_1, h_lead1_to_center)
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self_energy2, gamma2 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_2, h01_for_lead_1, h_lead2_to_center)
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self_energy3, gamma3 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_3, h01_for_lead_1, h_lead3_to_center)
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self_energy4, gamma4 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_4, h01_for_lead_1, h_lead4_to_center)
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self_energy5, gamma5 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_5, h01_for_lead_1, h_lead5_to_center)
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self_energy6, gamma6 = guan.self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00_for_lead_6, h01_for_lead_1, h_lead6_to_center)
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gamma_array = [gamma1, gamma2, gamma3, gamma4, gamma5, gamma6]
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green = np.linalg.inv(fermi_energy*np.eye(internal_degree*width*length)-center_hamiltonian-self_energy1-self_energy2-self_energy3-self_energy4-self_energy5-self_energy6)
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return gamma_array, green
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# 计算六端口的透射矩阵
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def calculate_six_terminal_transmission_matrix(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
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import numpy as np
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import guan
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gamma_array, green = guan.get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width, length, internal_degree, moving_step_of_leads)
|
||
transmission_matrix = np.zeros((6, 6), dtype=complex)
|
||
channel_lead_4 = guan.calculate_conductance(fermi_energy, h00_for_lead_4, h01_for_lead_4, length=3)
|
||
channel_lead_2 = guan.calculate_conductance(fermi_energy, h00_for_lead_2, h01_for_lead_2, length=3)
|
||
for i0 in range(6):
|
||
for j0 in range(6):
|
||
if j0!=i0:
|
||
transmission_matrix[i0, j0] = np.trace(np.dot(np.dot(np.dot(gamma_array[i0], green), gamma_array[j0]), green.transpose().conj()))
|
||
for i0 in range(6):
|
||
if i0 == 0 or i0 == 3:
|
||
transmission_matrix[i0, i0] = channel_lead_4
|
||
else:
|
||
transmission_matrix[i0, i0] = channel_lead_2
|
||
for i0 in range(6):
|
||
for j0 in range(6):
|
||
if j0!=i0:
|
||
transmission_matrix[i0, i0] = transmission_matrix[i0, i0]-transmission_matrix[i0, j0]
|
||
transmission_matrix = np.real(transmission_matrix)
|
||
return transmission_matrix
|
||
|
||
# 计算从电极1出发的透射系数
|
||
def calculate_six_terminal_transmissions_from_lead_1(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10):
|
||
import numpy as np
|
||
import guan
|
||
gamma_array, green = guan.get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width, length, internal_degree, moving_step_of_leads)
|
||
transmission_12 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[1]), green.transpose().conj())))
|
||
transmission_13 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[2]), green.transpose().conj())))
|
||
transmission_14 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[3]), green.transpose().conj())))
|
||
transmission_15 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[4]), green.transpose().conj())))
|
||
transmission_16 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[5]), green.transpose().conj())))
|
||
return transmission_12, transmission_13, transmission_14, transmission_15, transmission_16
|
||
|
||
# 通过动量k的虚部，判断通道为传播通道还是衰减通道
|
||
def if_active_channel(k_of_channel):
|
||
import numpy as np
|
||
if np.abs(np.imag(k_of_channel))<1e-6:
|
||
if_active = 1
|
||
else:
|
||
if_active = 0
|
||
return if_active
|
||
|
||
# 获取通道的动量和速度，用于计算散射矩阵
|
||
def get_k_and_velocity_of_channel(fermi_energy, h00, h01):
|
||
import numpy as np
|
||
import math
|
||
import copy
|
||
import guan
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
transfer = guan.transfer_matrix(fermi_energy, h00, h01)
|
||
eigenvalue, eigenvector = np.linalg.eig(transfer)
|
||
k_of_channel = np.log(eigenvalue)/1j
|
||
ind = np.argsort(np.real(k_of_channel))
|
||
k_of_channel = np.sort(k_of_channel)
|
||
temp = np.zeros((2*dim, 2*dim), dtype=complex)
|
||
temp2 = np.zeros((2*dim), dtype=complex)
|
||
i0 = 0
|
||
for ind0 in ind:
|
||
temp[:, i0] = eigenvector[:, ind0]
|
||
temp2[i0] = eigenvalue[ind0]
|
||
i0 += 1
|
||
eigenvalue = copy.deepcopy(temp2)
|
||
temp = temp[0:dim, :]
|
||
factor = np.zeros(2*dim)
|
||
for dim0 in range(dim):
|
||
factor = factor+np.square(np.abs(temp[dim0, :]))
|
||
for dim0 in range(2*dim):
|
||
temp[:, dim0] = temp[:, dim0]/math.sqrt(factor[dim0])
|
||
velocity_of_channel = np.zeros((2*dim), dtype=complex)
|
||
for dim0 in range(2*dim):
|
||
velocity_of_channel[dim0] = eigenvalue[dim0]*np.dot(np.dot(temp[0:dim, :].transpose().conj(), h01),temp[0:dim, :])[dim0, dim0]
|
||
velocity_of_channel = -2*np.imag(velocity_of_channel)
|
||
eigenvector = copy.deepcopy(temp)
|
||
return k_of_channel, velocity_of_channel, eigenvalue, eigenvector
|
||
|
||
# 获取分类后的动量和速度，以及U和F，用于计算散射矩阵
|
||
def get_classified_k_velocity_u_and_f(fermi_energy, h00, h01):
|
||
import numpy as np
|
||
import guan
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
k_of_channel, velocity_of_channel, eigenvalue, eigenvector = guan.get_k_and_velocity_of_channel(fermi_energy, h00, h01)
|
||
ind_right_active = 0; ind_right_evanescent = 0; ind_left_active = 0; ind_left_evanescent = 0
|
||
k_right = np.zeros(dim, dtype=complex); k_left = np.zeros(dim, dtype=complex)
|
||
velocity_right = np.zeros(dim, dtype=complex); velocity_left = np.zeros(dim, dtype=complex)
|
||
lambda_right = np.zeros(dim, dtype=complex); lambda_left = np.zeros(dim, dtype=complex)
|
||
u_right = np.zeros((dim, dim), dtype=complex); u_left = np.zeros((dim, dim), dtype=complex)
|
||
for dim0 in range(2*dim):
|
||
if_active = guan.if_active_channel(k_of_channel[dim0])
|
||
if guan.if_active_channel(k_of_channel[dim0]) == 1:
|
||
direction = np.sign(velocity_of_channel[dim0])
|
||
else:
|
||
direction = np.sign(np.imag(k_of_channel[dim0]))
|
||
if direction == 1:
|
||
if if_active == 1: # right-moving active channel
|
||
k_right[ind_right_active] = k_of_channel[dim0]
|
||
velocity_right[ind_right_active] = velocity_of_channel[dim0]
|
||
lambda_right[ind_right_active] = eigenvalue[dim0]
|
||
u_right[:, ind_right_active] = eigenvector[:, dim0]
|
||
ind_right_active += 1
|
||
else: # right-moving evanescent channel
|
||
k_right[dim-1-ind_right_evanescent] = k_of_channel[dim0]
|
||
velocity_right[dim-1-ind_right_evanescent] = velocity_of_channel[dim0]
|
||
lambda_right[dim-1-ind_right_evanescent] = eigenvalue[dim0]
|
||
u_right[:, dim-1-ind_right_evanescent] = eigenvector[:, dim0]
|
||
ind_right_evanescent += 1
|
||
else:
|
||
if if_active == 1: # left-moving active channel
|
||
k_left[ind_left_active] = k_of_channel[dim0]
|
||
velocity_left[ind_left_active] = velocity_of_channel[dim0]
|
||
lambda_left[ind_left_active] = eigenvalue[dim0]
|
||
u_left[:, ind_left_active] = eigenvector[:, dim0]
|
||
ind_left_active += 1
|
||
else: # left-moving evanescent channel
|
||
k_left[dim-1-ind_left_evanescent] = k_of_channel[dim0]
|
||
velocity_left[dim-1-ind_left_evanescent] = velocity_of_channel[dim0]
|
||
lambda_left[dim-1-ind_left_evanescent] = eigenvalue[dim0]
|
||
u_left[:, dim-1-ind_left_evanescent] = eigenvector[:, dim0]
|
||
ind_left_evanescent += 1
|
||
lambda_matrix_right = np.diag(lambda_right)
|
||
lambda_matrix_left = np.diag(lambda_left)
|
||
f_right = np.dot(np.dot(u_right, lambda_matrix_right), np.linalg.inv(u_right))
|
||
f_left = np.dot(np.dot(u_left, lambda_matrix_left), np.linalg.inv(u_left))
|
||
return k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active
|
||
|
||
# 计算散射矩阵
|
||
def calculate_scattering_matrix(fermi_energy, h00, h01, length=100):
|
||
import numpy as np
|
||
import math
|
||
import copy
|
||
import guan
|
||
h01 = np.array(h01)
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
|
||
k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active = guan.get_classified_k_velocity_u_and_f(fermi_energy, h00, h01)
|
||
right_self_energy = np.dot(h01, f_right)
|
||
left_self_energy = np.dot(h01.transpose().conj(), np.linalg.inv(f_left))
|
||
for i0 in range(length):
|
||
if i0 == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_00_n = copy.deepcopy(green_nn_n)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
green_n0_n = copy.deepcopy(green_nn_n)
|
||
elif i0 != length-1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_00_n = guan.green_function_ii_n(green_00_n, green_0n_n, h01, green_nn_n, green_n0_n)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
green_n0_n = guan.green_function_ni_n(green_nn_n, h01, green_n0_n)
|
||
temp = np.dot(h01.transpose().conj(), np.linalg.inv(f_right)-np.linalg.inv(f_left))
|
||
transmission_matrix = np.dot(np.dot(np.linalg.inv(u_right), np.dot(green_n0_n, temp)), u_right)
|
||
reflection_matrix = np.dot(np.dot(np.linalg.inv(u_left), np.dot(green_00_n, temp)-np.identity(dim)), u_right)
|
||
for dim0 in range(dim):
|
||
for dim1 in range(dim):
|
||
if_active = guan.if_active_channel(k_right[dim0])*guan.if_active_channel(k_right[dim1])
|
||
if if_active == 1:
|
||
transmission_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_right[dim0]/velocity_right[dim1])) * transmission_matrix[dim0, dim1]
|
||
reflection_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_left[dim0]/velocity_right[dim1]))*reflection_matrix[dim0, dim1]
|
||
else:
|
||
transmission_matrix[dim0, dim1] = 0
|
||
reflection_matrix[dim0, dim1] = 0
|
||
sum_of_tran_refl_array = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)+np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
for sum_of_tran_refl in sum_of_tran_refl_array:
|
||
if sum_of_tran_refl > 1.001:
|
||
print('Error Alert: scattering matrix is not normalized!')
|
||
return transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active
|
||
|
||
# 从散射矩阵中，获取散射矩阵的信息
|
||
def information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active):
|
||
import numpy as np
|
||
if np.array(transmission_matrix).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(transmission_matrix).shape[0]
|
||
number_of_active_channels = ind_right_active
|
||
number_of_evanescent_channels = dim-ind_right_active
|
||
k_of_right_moving_active_channels = np.real(k_right[0:ind_right_active])
|
||
k_of_left_moving_active_channels = np.real(k_left[0:ind_right_active])
|
||
velocity_of_right_moving_active_channels = np.real(velocity_right[0:ind_right_active])
|
||
velocity_of_left_moving_active_channels = np.real(velocity_left[0:ind_right_active])
|
||
transmission_matrix_for_active_channels = np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active]))
|
||
reflection_matrix_for_active_channels = np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active]))
|
||
total_transmission_of_channels = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
total_conductance = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])))
|
||
total_reflection_of_channels = np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
sum_of_transmission_and_reflection_of_channels = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0) + np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
return number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels
|
||
|
||
# 已知h00和h01，计算散射矩阵并获得散射矩阵的信息
|
||
def calculate_scattering_matrix_and_get_information(fermi_energy, h00, h01, length=100):
|
||
import guan
|
||
transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix(fermi_energy, h00, h01, length=length)
|
||
|
||
number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)
|
||
|
||
return number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels
|
||
|
||
# 从散射矩阵中打印出散射矩阵的信息
|
||
def print_or_write_scattering_matrix_with_information_of_scattering_matrix(number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels, print_show=1, write_file=0, filename='a', file_format='.txt'):
|
||
if print_show == 1:
|
||
print('\nActive channel (left or right) = ', number_of_active_channels)
|
||
print('Evanescent channel (left or right) = ', number_of_evanescent_channels, '\n')
|
||
print('K of right-moving active channels:\n', k_of_right_moving_active_channels)
|
||
print('K of left-moving active channels:\n', k_of_left_moving_active_channels, '\n')
|
||
print('Velocity of right-moving active channels:\n', velocity_of_right_moving_active_channels)
|
||
print('Velocity of left-moving active channels:\n', velocity_of_left_moving_active_channels, '\n')
|
||
print('Transmission matrix:\n', transmission_matrix_for_active_channels)
|
||
print('Reflection matrix:\n', reflection_matrix_for_active_channels, '\n')
|
||
print('Total transmission of channels:\n', total_transmission_of_channels)
|
||
print('Total conductance = ', total_conductance, '\n')
|
||
print('Total reflection of channels:\n', total_reflection_of_channels)
|
||
print('Sum of transmission and reflection of channels:\n', sum_of_transmission_and_reflection_of_channels, '\n')
|
||
if write_file == 1:
|
||
with open(filename+file_format, 'w') as f:
|
||
f.write('Active channel (left or right) = ' + str(number_of_active_channels) + '\n')
|
||
f.write('Evanescent channel (left or right) = ' + str(number_of_evanescent_channels) + '\n\n')
|
||
f.write('Channel K Velocity\n')
|
||
for ind0 in range(number_of_active_channels):
|
||
f.write(' '+str(ind0 + 1) + ' | '+str(k_of_right_moving_active_channels[ind0])+' ' + str(velocity_of_right_moving_active_channels[ind0])+'\n')
|
||
f.write('\n')
|
||
for ind0 in range(number_of_active_channels):
|
||
f.write(' -' + str(ind0 + 1) + ' | ' + str(k_of_left_moving_active_channels[ind0]) + ' ' + str(velocity_of_left_moving_active_channels[ind0]) + '\n')
|
||
f.write('\nScattering matrix:\n ')
|
||
for ind0 in range(number_of_active_channels):
|
||
f.write(str(ind0+1)+' ')
|
||
f.write('\n')
|
||
for ind1 in range(number_of_active_channels):
|
||
f.write(' '+str(ind1+1)+' ')
|
||
for ind2 in range(number_of_active_channels):
|
||
f.write('%f' % transmission_matrix_for_active_channels[ind1, ind2]+' ')
|
||
f.write('\n')
|
||
f.write('\n')
|
||
for ind1 in range(number_of_active_channels):
|
||
f.write(' -'+str(ind1+1)+' ')
|
||
for ind2 in range(number_of_active_channels):
|
||
f.write('%f' % reflection_matrix_for_active_channels[ind1, ind2]+' ')
|
||
f.write('\n')
|
||
f.write('\n')
|
||
f.write('Total transmission of channels:\n'+str(total_transmission_of_channels)+'\n')
|
||
f.write('Total conductance = '+str(total_conductance)+'\n')
|
||
|
||
# 已知h00和h01，计算散射矩阵并打印出散射矩阵的信息
|
||
def print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, print_show=1, write_file=0, filename='a', file_format='.txt'):
|
||
import guan
|
||
transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix(fermi_energy, h00, h01, length=length)
|
||
|
||
number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)
|
||
|
||
guan.print_or_write_scattering_matrix_with_information_of_scattering_matrix(number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels, print_show=print_show, write_file=write_file, filename=filename, file_format=file_format)
|
||
|
||
# 在无序下，计算散射矩阵
|
||
def calculate_scattering_matrix_with_disorder(fermi_energy, h00, h01, length=100, disorder_intensity=2.0, disorder_concentration=1.0):
|
||
import numpy as np
|
||
import math
|
||
import copy
|
||
import guan
|
||
h01 = np.array(h01)
|
||
if np.array(h00).shape==():
|
||
dim = 1
|
||
else:
|
||
dim = np.array(h00).shape[0]
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k_right, k_left, velocity_right, velocity_left, f_right, f_left, u_right, u_left, ind_right_active = guan.get_classified_k_velocity_u_and_f(fermi_energy, h00, h01)
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right_self_energy = np.dot(h01, f_right)
|
||
left_self_energy = np.dot(h01.transpose().conj(), np.linalg.inv(f_left))
|
||
for i0 in range(length):
|
||
disorder = np.zeros((dim, dim))
|
||
for dim0 in range(dim):
|
||
if np.random.uniform(0, 1)<=disorder_concentration:
|
||
disorder[dim0, dim0] = np.random.uniform(-disorder_intensity, disorder_intensity)
|
||
if i0 == 0:
|
||
green_nn_n = guan.green_function(fermi_energy, h00, broadening=0, self_energy=left_self_energy)
|
||
green_00_n = copy.deepcopy(green_nn_n)
|
||
green_0n_n = copy.deepcopy(green_nn_n)
|
||
green_n0_n = copy.deepcopy(green_nn_n)
|
||
elif i0 != length-1:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00+disorder, h01, green_nn_n, broadening=0)
|
||
else:
|
||
green_nn_n = guan.green_function_nn_n(fermi_energy, h00, h01, green_nn_n, broadening=0, self_energy=right_self_energy)
|
||
green_00_n = guan.green_function_ii_n(green_00_n, green_0n_n, h01, green_nn_n, green_n0_n)
|
||
green_0n_n = guan.green_function_in_n(green_0n_n, h01, green_nn_n)
|
||
green_n0_n = guan.green_function_ni_n(green_nn_n, h01, green_n0_n)
|
||
temp = np.dot(h01.transpose().conj(), np.linalg.inv(f_right)-np.linalg.inv(f_left))
|
||
transmission_matrix = np.dot(np.dot(np.linalg.inv(u_right), np.dot(green_n0_n, temp)), u_right)
|
||
reflection_matrix = np.dot(np.dot(np.linalg.inv(u_left), np.dot(green_00_n, temp)-np.identity(dim)), u_right)
|
||
for dim0 in range(dim):
|
||
for dim1 in range(dim):
|
||
if_active = guan.if_active_channel(k_right[dim0])*guan.if_active_channel(k_right[dim1])
|
||
if if_active == 1:
|
||
transmission_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_right[dim0]/velocity_right[dim1])) * transmission_matrix[dim0, dim1]
|
||
reflection_matrix[dim0, dim1] = math.sqrt(np.abs(velocity_left[dim0]/velocity_right[dim1]))*reflection_matrix[dim0, dim1]
|
||
else:
|
||
transmission_matrix[dim0, dim1] = 0
|
||
reflection_matrix[dim0, dim1] = 0
|
||
sum_of_tran_refl_array = np.sum(np.square(np.abs(transmission_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)+np.sum(np.square(np.abs(reflection_matrix[0:ind_right_active, 0:ind_right_active])), axis=0)
|
||
for sum_of_tran_refl in sum_of_tran_refl_array:
|
||
if sum_of_tran_refl > 1.001:
|
||
print('Error Alert: scattering matrix is not normalized!')
|
||
return transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active
|
||
|
||
# 在无序下，计算散射矩阵，并获取散射矩阵多次计算的平均信息
|
||
def calculate_scattering_matrix_with_disorder_and_get_averaged_information(fermi_energy, h00, h01, length=100, disorder_intensity=2.0, disorder_concentration=1.0, calculation_times=1):
|
||
import guan
|
||
transmission_matrix_for_active_channels_averaged = 0
|
||
reflection_matrix_for_active_channels_averaged = 0
|
||
for i0 in range(calculation_times):
|
||
transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix_with_disorder(fermi_energy, h00, h01, length, disorder_intensity, disorder_concentration)
|
||
|
||
number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active)
|
||
|
||
transmission_matrix_for_active_channels_averaged += transmission_matrix_for_active_channels
|
||
reflection_matrix_for_active_channels_averaged += reflection_matrix_for_active_channels
|
||
transmission_matrix_for_active_channels_averaged = transmission_matrix_for_active_channels_averaged/calculation_times
|
||
reflection_matrix_for_active_channels_averaged = reflection_matrix_for_active_channels_averaged/calculation_times
|
||
return transmission_matrix_for_active_channels_averaged, reflection_matrix_for_active_channels_averaged |