def main():
N = 30
a = 1
hamiltonian_function0 = functools.partial(hamiltonian,
k=0,
N=N,
M=0,
t1=1,
a=a)
B_array = np.linspace(0, 1 / (3 * np.sqrt(3) / 2 * a * a), 100)
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(
B_array, hamiltonian_function0)
BS_array = B_array * (3 * np.sqrt(3) / 2 * a * a)
guan.plot(BS_array,
eigenvalue_array,
xlabel='Flux (BS/phi_0)',
ylabel='E',
title='Ny=%i' % N,
filename='a',
show=1,
save=0,
type='k.',
y_min=None,
y_max=None,
markersize=3)
def main():
Ny = 21
k_array = np.linspace(-pi, pi, 100)
H_k = functools.partial(hamiltonian, ky=0, Ny=Ny, B=1 / Ny)
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(
k_array, H_k)
guan.plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', type='k')
H_k = functools.partial(hamiltonian, Ny=Ny, B=1 / Ny)
chern_number = guan.calculate_chern_number_for_square_lattice(
H_k, precision=100)
print(chern_number)
print(sum(chern_number))
def main():
Num_kx = 100
Num_ky = 100
kx_array = np.linspace(-pi, pi, Num_kx)
ky_array = np.linspace(-pi, pi, Num_ky)
nu_x_array = []
for ky in ky_array:
vector1_array = []
vector2_array = []
for kx in kx_array:
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian(kx, ky))
if kx != pi:
vector1_array.append(eigenvector[:, 0])
vector2_array.append(eigenvector[:, 1])
else:
# 这里是为了-pi和pi有相同的波函数，使得Wilson loop的值与波函数规范无关。
vector1_array.append(vector1_array[0])
vector2_array.append(vector2_array[0])
W_x_k = np.eye(2, dtype=complex)
for i0 in range(Num_kx - 1):
F = np.zeros((2, 2), dtype=complex)
F[0, 0] = np.dot(vector1_array[i0 + 1].transpose().conj(),
vector1_array[i0])
F[1, 1] = np.dot(vector2_array[i0 + 1].transpose().conj(),
vector2_array[i0])
F[0, 1] = np.dot(vector1_array[i0 + 1].transpose().conj(),
vector2_array[i0])
F[1, 0] = np.dot(vector2_array[i0 + 1].transpose().conj(),
vector1_array[i0])
W_x_k = np.dot(F, W_x_k)
eigenvalue, eigenvector = np.linalg.eig(W_x_k)
nu_x = np.log(eigenvalue) / 2 / pi / 1j
for i0 in range(2):
if np.real(nu_x[i0]) < 0:
nu_x[i0] += 1
nu_x = np.sort(nu_x)
nu_x_array.append(nu_x.real)
import guan
guan.plot(ky_array,
nu_x_array,
xlabel='ky',
ylabel='nu_x',
type='-',
y_min=0,
y_max=1)
def main():
kx = np.arange(-pi, pi, 0.05)
ky = np.arange(-pi, pi, 0.05)
eigenvalue_array = guan.calculate_eigenvalue_with_two_parameters(
kx, ky, hamiltonian)
guan.plot_3d_surface(kx,
ky,
eigenvalue_array,
xlabel='kx',
ylabel='ky',
zlabel='E',
title='BBH bands')
hamiltonian0 = functools.partial(hamiltonian, ky=0)
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(
kx, hamiltonian0)
guan.plot(kx,
eigenvalue_array,
xlabel='kx',
ylabel='E',
title='BBH bands ky=0')
import numpy as np
from math import *
import cmath
import guan
v = 0.6
w = 1
k_array = np.linspace(-pi, pi, 100)
def hamiltonian_1(k):
matrix = np.zeros((2, 2), dtype=complex)
matrix[0, 1] = v + w * cmath.exp(-1j * k)
matrix[1, 0] = v + w * cmath.exp(1j * k)
return matrix
def hamiltonian_2(k):
matrix = np.zeros((2, 2), dtype=complex)
matrix[0, 1] = v * cmath.exp(1j * k / 2) + w * cmath.exp(-1j * k / 2)
matrix[1, 0] = v * cmath.exp(-1j * k / 2) + w * cmath.exp(1j * k / 2)
return matrix
E_1_array = guan.calculate_eigenvalue_with_one_parameter(
k_array, hamiltonian_1)
guan.plot(k_array, E_1_array, xlabel='k', ylabel='E_1')
E_2_array = guan.calculate_eigenvalue_with_one_parameter(
k_array, hamiltonian_2)
guan.plot(k_array, E_2_array, xlabel='k', ylabel='E_2')
def main():
start_time = time.time()
width = 21
length = 72
fermi_energy_array = np.arange(-4, 4, .05)
# 中心区的哈密顿量
H_cetner = get_center_hamiltonian(Nx=length, Ny=width, B=1 / width)
# 电极的h00和h01
lead_h00 = get_lead_h00(width)
lead_h01 = get_lead_h01(width)
transmission_12_array = []
transmission_13_array = []
transmission_14_array = []
transmission_15_array = []
transmission_16_array = []
transmission_1_all_array = []
for fermi_energy in fermi_energy_array:
print(fermi_energy)
# 几何形状如下所示：
# lead2 lead3
# lead1(L) lead4(R)
# lead6 lead5
# 电极到中心区的跃迁矩阵
h_lead1_to_center = np.zeros((width, width * length), dtype=complex)
h_lead2_to_center = np.zeros((width, width * length), dtype=complex)
h_lead3_to_center = np.zeros((width, width * length), dtype=complex)
h_lead4_to_center = np.zeros((width, width * length), dtype=complex)
h_lead5_to_center = np.zeros((width, width * length), dtype=complex)
h_lead6_to_center = np.zeros((width, width * length), dtype=complex)
move = 10 # the step of leads 2,3,6,5 moving to center
for i0 in range(width):
h_lead1_to_center[i0, i0] = 1
h_lead2_to_center[i0, width * (move + i0) + (width - 1)] = 1
h_lead3_to_center[i0, width * (length - move - 1 - i0) +
(width - 1)] = 1
h_lead4_to_center[i0, width * (length - 1) + i0] = 1
h_lead5_to_center[i0, width * (length - move - 1 - i0) + 0] = 1
h_lead6_to_center[i0, width * (i0 + move) + 0] = 1
# 自能
self_energy1, gamma1 = guan.self_energy_of_lead_with_h_lead_to_center(
fermi_energy, lead_h00, lead_h01, h_lead1_to_center)
self_energy2, gamma2 = guan.self_energy_of_lead_with_h_lead_to_center(
fermi_energy, lead_h00, lead_h01, h_lead2_to_center)
self_energy3, gamma3 = guan.self_energy_of_lead_with_h_lead_to_center(
fermi_energy, lead_h00, lead_h01, h_lead3_to_center)
self_energy4, gamma4 = guan.self_energy_of_lead_with_h_lead_to_center(
fermi_energy, lead_h00, lead_h01, h_lead4_to_center)
self_energy5, gamma5 = guan.self_energy_of_lead_with_h_lead_to_center(
fermi_energy, lead_h00, lead_h01, h_lead5_to_center)
self_energy6, gamma6 = guan.self_energy_of_lead_with_h_lead_to_center(
fermi_energy, lead_h00, lead_h01, h_lead6_to_center)
# 整体格林函数
green = np.linalg.inv(fermi_energy * np.eye(width * length) -
H_cetner - self_energy1 - self_energy2 -
self_energy3 - self_energy4 - self_energy5 -
self_energy6)
# Transmission
transmission_12 = np.trace(
np.dot(np.dot(np.dot(gamma1, green), gamma2),
green.transpose().conj()))
transmission_13 = np.trace(
np.dot(np.dot(np.dot(gamma1, green), gamma3),
green.transpose().conj()))
transmission_14 = np.trace(
np.dot(np.dot(np.dot(gamma1, green), gamma4),
green.transpose().conj()))
transmission_15 = np.trace(
np.dot(np.dot(np.dot(gamma1, green), gamma5),
green.transpose().conj()))
transmission_16 = np.trace(
np.dot(np.dot(np.dot(gamma1, green), gamma6),
green.transpose().conj()))
transmission_12_array.append(np.real(transmission_12))
transmission_13_array.append(np.real(transmission_13))
transmission_14_array.append(np.real(transmission_14))
transmission_15_array.append(np.real(transmission_15))
transmission_16_array.append(np.real(transmission_16))
transmission_1_all_array.append(
np.real(transmission_12 + transmission_13 + transmission_14 +
transmission_15 + transmission_16))
guan.plot(fermi_energy_array,
transmission_12_array,
xlabel='Fermi energy',
ylabel='Transmission_12')
guan.plot(fermi_energy_array,
transmission_13_array,
xlabel='Fermi energy',
ylabel='Transmission_13')
guan.plot(fermi_energy_array,
transmission_14_array,
xlabel='Fermi energy',
ylabel='Transmission_14')
guan.plot(fermi_energy_array,
transmission_15_array,
xlabel='Fermi energy',
ylabel='Transmission_15')
guan.plot(fermi_energy_array,
transmission_16_array,
xlabel='Fermi energy',
ylabel='Transmission_16')
guan.plot(fermi_energy_array,
transmission_1_all_array,
xlabel='Fermi energy',
ylabel='Transmission_1_all')
end_time = time.time()
print('运行时间=', end_time - start_time)
import guan
import numpy as np
fermi_energy_array = np.linspace(-4, 4, 400)
h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(4)
h01 = np.identity(4)
conductance_array = guan.calculate_conductance_with_fermi_energy_array(
fermi_energy_array, h00, h01)
guan.plot(fermi_energy_array,
conductance_array,
xlabel='E',
ylabel='Conductance',
type='-')
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
center_hamiltonian = get_center_hamiltonian(Nx=length, Ny=width)
# 电极的h00和h01
lead_h00 = get_lead_h00(width)
lead_h01 = get_lead_h01(width)
transmission_12_array = []
transmission_13_array = []
transmission_14_array = []
transmission_15_array = []
transmission_16_array = []
transmission_1_all_array = []
for fermi_energy in fermi_energy_array:
print(fermi_energy)
# 几何形状如下所示：
# lead2 lead3
# lead1(L) lead4(R)
# lead6 lead5
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)
transmission_12_array.append(transmission_matrix[0, 1])
transmission_13_array.append(transmission_matrix[0, 2])
transmission_14_array.append(transmission_matrix[0, 3])
transmission_15_array.append(transmission_matrix[0, 4])
transmission_16_array.append(transmission_matrix[0, 5])
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])
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)
def main():
Num_kx = 30 # for wilson loop and nested wilson loop
Num_ky = 30 # for wilson loop and nested wilson loop
Num_kx2 = 20 # plot precision
Num_ky2 = 20 # plot precision
kx_array = np.linspace(-pi, pi, Num_kx)
ky_array = np.linspace(-pi, pi, Num_ky)
kx2_array = np.linspace(-pi, pi, Num_kx2)
ky2_array = np.linspace(-pi, pi, Num_ky2)
# Part I: calculate p_y_for_nu_x
p_y_for_nu_x_array = []
for kx in kx2_array:
print('kx=', kx)
w_vector_for_nu1_array = []
vector1_array = []
vector2_array = []
i0 = -1
for ky in ky_array:
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian(kx, ky))
if ky != pi:
vector1_array.append(eigenvector[:, 0])
vector2_array.append(eigenvector[:, 1])
else:
vector1_array.append(vector1_array[0])
vector2_array.append(vector2_array[0])
i0 = 0
for ky in ky_array:
if ky != pi:
nu_x_vector_1, nu_x_vector_2 = get_nu_x_vector(kx_array, ky)
# the Wannier band subspaces
w_vector_for_nu1 = vector1_array[i0] * nu_x_vector_1[
0] + vector2_array[i0] * nu_x_vector_1[1]
w_vector_for_nu1_array.append(w_vector_for_nu1)
else:
w_vector_for_nu1_array.append(w_vector_for_nu1_array[0])
i0 += 1
W_y_k_for_nu_x = 1
for i0 in range(Num_ky - 1):
F_for_nu_x = np.dot(
w_vector_for_nu1_array[i0 + 1].transpose().conj(),
w_vector_for_nu1_array[i0])
W_y_k_for_nu_x = F_for_nu_x * W_y_k_for_nu_x
p_y_for_nu_x = np.log(W_y_k_for_nu_x) / 2 / pi / 1j
if np.real(p_y_for_nu_x) < 0:
p_y_for_nu_x += 1
p_y_for_nu_x_array.append(p_y_for_nu_x.real)
print('p_y_for_nu_x=', p_y_for_nu_x)
guan.plot(kx2_array,
p_y_for_nu_x_array,
xlabel='kx',
ylabel='p_y_for_nu_x',
type='-o',
y_min=0,
y_max=1)
# Part II: calculate p_x_for_nu_y
p_x_for_nu_y_array = []
for ky in ky2_array:
w_vector_for_nu1_array = []
vector1_array = []
vector2_array = []
for kx in kx_array:
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian(kx, ky))
if kx != pi:
vector1_array.append(eigenvector[:, 0])
vector2_array.append(eigenvector[:, 1])
else:
vector1_array.append(vector1_array[0])
vector2_array.append(vector2_array[0])
i0 = 0
for kx in kx_array:
if kx != pi:
nu_y_vector_1, nu_y_vector_2 = get_nu_y_vector(kx, ky_array)
# the Wannier band subspaces
w_vector_for_nu1 = vector1_array[i0] * nu_y_vector_1[
0] + vector2_array[i0] * nu_y_vector_1[1]
w_vector_for_nu1_array.append(w_vector_for_nu1)
else:
w_vector_for_nu1_array.append(w_vector_for_nu1_array[0])
i0 += 1
W_x_k_for_nu_y = 1
for i0 in range(Num_ky - 1):
F_for_nu_y = np.dot(
w_vector_for_nu1_array[i0 + 1].transpose().conj(),
w_vector_for_nu1_array[i0])
W_x_k_for_nu_y = F_for_nu_y * W_x_k_for_nu_y
p_x_for_nu_y = np.log(W_x_k_for_nu_y) / 2 / pi / 1j
if np.real(p_x_for_nu_y) < 0:
p_x_for_nu_y += 1
p_x_for_nu_y_array.append(p_x_for_nu_y.real)
print('p_x_for_nu_y=', p_x_for_nu_y)
# print(sum(p_x_for_nu_y_array)/len(p_x_for_nu_y_array))
guan.plot(ky2_array,
p_x_for_nu_y_array,
xlabel='ky',
ylabel='p_x_for_nu_y',
type='-o',
y_min=0,
y_max=1)