update

Tutorial/0_test.py

@@ -1,3 +1,3 @@
-import gjh
+import gjh
-
+
 gjh.test()

Tutorial/10_Wilson_loop.py

@@ -1,20 +1,20 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-import cmath
+import cmath
-from math import *
+from math import *
-
+
-def hamiltonian_function(k): # SSH model
+def hamiltonian_function(k): # SSH model
-    gamma = 0.5
+    gamma = 0.5
-    lambda0 = 1
+    lambda0 = 1
-    delta = 0
+    delta = 0
-    hamiltonian = np.zeros((2, 2), dtype=complex)
+    hamiltonian = np.zeros((2, 2), dtype=complex)
-    hamiltonian[0,0] = delta
+    hamiltonian[0,0] = delta
-    hamiltonian[1,1] = -delta
+    hamiltonian[1,1] = -delta
-    hamiltonian[0,1] = gamma+lambda0*cmath.exp(-1j*k)
+    hamiltonian[0,1] = gamma+lambda0*cmath.exp(-1j*k)
-    hamiltonian[1,0] = gamma+lambda0*cmath.exp(1j*k)
+    hamiltonian[1,0] = gamma+lambda0*cmath.exp(1j*k)
-    return hamiltonian
+    return hamiltonian
-
+
-wilson_loop_array = gjh.calculate_wilson_loop(hamiltonian_function)
+wilson_loop_array = gjh.calculate_wilson_loop(hamiltonian_function)
-print('wilson loop =', wilson_loop_array)
+print('wilson loop =', wilson_loop_array)
-p = np.log(wilson_loop_array)/2/pi/1j
+p = np.log(wilson_loop_array)/2/pi/1j
 print('p =', p, '\n')

Tutorial/11_read_and_write.py

@@ -1,20 +1,20 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-
+
-x = np.array([1, 2, 3])
+x = np.array([1, 2, 3])
-y = np.array([5, 6, 7])
+y = np.array([5, 6, 7])
-gjh.write_one_dimensional_data(x, y, filename='one_dimensional_data')
+gjh.write_one_dimensional_data(x, y, filename='one_dimensional_data')
-
+
-matrix = np.zeros((3, 3))
+matrix = np.zeros((3, 3))
-matrix[0, 1] = 11
+matrix[0, 1] = 11
-gjh.write_two_dimensional_data(x, y, matrix, filename='two_dimensional_data')
+gjh.write_two_dimensional_data(x, y, matrix, filename='two_dimensional_data')
-
+
-
+
-x_read, y_read = gjh.read_one_dimensional_data('one_dimensional_data')
+x_read, y_read = gjh.read_one_dimensional_data('one_dimensional_data')
-print(x_read, '\n')
+print(x_read, '\n')
-print(y_read, '\n\n')
+print(y_read, '\n\n')
-
+
-x_read, y_read, matrix_read = gjh.read_two_dimensional_data('two_dimensional_data')
+x_read, y_read, matrix_read = gjh.read_two_dimensional_data('two_dimensional_data')
-print(x_read, '\n')
+print(x_read, '\n')
-print(y_read, '\n')
+print(y_read, '\n')
 print(matrix_read)

Tutorial/12_download.py

@@ -0,0 +1,5 @@
+import gjh
+
+gjh.download_with_scihub()
+# gjh.download_with_scihub('address')
+# gjh.download_with_scihub(num=3)

Tutorial/1_Pauli_matrix.py

@@ -1,6 +1,6 @@
-import gjh
+import gjh
-
+
-print('sigma_0:\n', gjh.sigma_0(), '\n')
+print('sigma_0:\n', gjh.sigma_0(), '\n')
-print('sigma_x:\n', gjh.sigma_x(), '\n')
+print('sigma_x:\n', gjh.sigma_x(), '\n')
-print('sigma_y:\n', gjh.sigma_y(), '\n')
+print('sigma_y:\n', gjh.sigma_y(), '\n')
 print('sigma_z:\n', gjh.sigma_z(), '\n')

Tutorial/2_Hamiltonian_of_finite_size.py

@@ -1,5 +1,5 @@
-import gjh
+import gjh
-
+
-print(gjh.finite_size_along_one_direction(3), '\n')
+print(gjh.finite_size_along_one_direction(3), '\n')
-print(gjh.finite_size_along_two_directions_for_square_lattice(2, 2), '\n')
+print(gjh.finite_size_along_two_directions_for_square_lattice(2, 2), '\n')
 print(gjh.finite_size_along_three_directions_for_cubic_lattice(2, 2, 2), '\n')

Tutorial/3_Fourier_transform_and_band_structures.py

@@ -1,19 +1,19 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-from math import *
+from math import *
-import functools
+import functools
-
+
-x = np.linspace(-pi, pi, 100)
+x = np.linspace(-pi, pi, 100)
-y = np.linspace(-pi, pi, 100)
+y = np.linspace(-pi, pi, 100)
-
+
-hamiltonian_function = functools.partial(gjh.one_dimensional_fourier_transform, unit_cell=0, hopping=1)
+hamiltonian_function = functools.partial(gjh.one_dimensional_fourier_transform, unit_cell=0, hopping=1)
-eigenvalue_array = gjh.calculate_eigenvalue_with_one_parameter(x, hamiltonian_function)
+eigenvalue_array = gjh.calculate_eigenvalue_with_one_parameter(x, hamiltonian_function)
-gjh.plot(x, eigenvalue_array, xlabel='k', ylabel='E', type='-o')
+gjh.plot(x, eigenvalue_array, xlabel='k', ylabel='E', type='-o')
-
+
-hamiltonian_function = functools.partial(gjh.two_dimensional_fourier_transform_for_square_lattice, unit_cell=0, hopping_1=1, hopping_2=1)
+hamiltonian_function = functools.partial(gjh.two_dimensional_fourier_transform_for_square_lattice, unit_cell=0, hopping_1=1, hopping_2=1)
-eigenvalue_array = gjh.calculate_eigenvalue_with_two_parameters(x, y, hamiltonian_function)
+eigenvalue_array = gjh.calculate_eigenvalue_with_two_parameters(x, y, hamiltonian_function)
-gjh.plot_3d_surface(x, y, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E')
+gjh.plot_3d_surface(x, y, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E')
-
+
-hamiltonian_function = functools.partial(gjh.three_dimensional_fourier_transform_for_cubic_lattice, k3=0, unit_cell=0, hopping_1=1, hopping_2=1, hopping_3=1)
+hamiltonian_function = functools.partial(gjh.three_dimensional_fourier_transform_for_cubic_lattice, k3=0, unit_cell=0, hopping_1=1, hopping_2=1, hopping_3=1)
-eigenvalue_array = gjh.calculate_eigenvalue_with_two_parameters(x, y, hamiltonian_function)
+eigenvalue_array = gjh.calculate_eigenvalue_with_two_parameters(x, y, hamiltonian_function)
 gjh.plot_3d_surface(x, y, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E')

Tutorial/4_bands_of_zigzag_graphene.py

@@ -1,12 +1,12 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-from math import *
+from math import *
-import functools
+import functools
-
+
-x = np.linspace(-pi, pi, 100)
+x = np.linspace(-pi, pi, 100)
-Ny = 10
+Ny = 10
-unit_cell = gjh.finite_size_along_two_directions_for_graphene(1, Ny)
+unit_cell = gjh.finite_size_along_two_directions_for_graphene(1, Ny)
-hopping = gjh.hopping_along_zigzag_direction_for_graphene(Ny)
+hopping = gjh.hopping_along_zigzag_direction_for_graphene(Ny)
-hamiltonian_function = functools.partial(gjh.one_dimensional_fourier_transform, unit_cell=unit_cell, hopping=hopping)
+hamiltonian_function = functools.partial(gjh.one_dimensional_fourier_transform, unit_cell=unit_cell, hopping=hopping)
-eigenvalue_array = gjh.calculate_eigenvalue_with_one_parameter(x, hamiltonian_function)
+eigenvalue_array = gjh.calculate_eigenvalue_with_one_parameter(x, hamiltonian_function)
 gjh.plot(x, eigenvalue_array, xlabel='k', ylabel='E')

Tutorial/5_total_density_of_states.py

@@ -1,7 +1,7 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-
+
-hamiltonian = gjh.finite_size_along_two_directions_for_square_lattice(2,2)
+hamiltonian = gjh.finite_size_along_two_directions_for_square_lattice(2,2)
-fermi_energy_array = np.linspace(-4, 4, 400)
+fermi_energy_array = np.linspace(-4, 4, 400)
-total_dos_array = gjh.total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.1)
+total_dos_array = gjh.total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.1)
 gjh.plot(fermi_energy_array, total_dos_array, xlabel='E', ylabel='Total DOS', type='-o')

Tutorial/6_local_density_of_states.py

@@ -1,28 +1,28 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-
+
-fermi_energy = 0
+fermi_energy = 0
-N1 = 3
+N1 = 3
-N2 = 4
+N2 = 4
-hamiltonian = gjh.finite_size_along_two_directions_for_square_lattice(N1,N2)
+hamiltonian = gjh.finite_size_along_two_directions_for_square_lattice(N1,N2)
-LDOS = gjh.local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2)
+LDOS = gjh.local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2)
-print('square lattice:\n', LDOS, '\n')
+print('square lattice:\n', LDOS, '\n')
-
+
-h00 = gjh.finite_size_along_one_direction(N2)
+h00 = gjh.finite_size_along_one_direction(N2)
-h01 = np.identity(N2)
+h01 = np.identity(N2)
-LDOS = gjh.local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00=h00, h01=h01, N2=N2, N1=N1)
+LDOS = gjh.local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00=h00, h01=h01, N2=N2, N1=N1)
-print(LDOS, '\n\n')
+print(LDOS, '\n\n')
-gjh.plot_contour(range(N1), range(N2), LDOS)
+gjh.plot_contour(range(N1), range(N2), LDOS)
-
+
-
+
-N1 = 3
+N1 = 3
-N2 = 4
+N2 = 4
-N3 = 5
+N3 = 5
-hamiltonian = gjh.finite_size_along_three_directions_for_cubic_lattice(N1, N2, N3)
+hamiltonian = gjh.finite_size_along_three_directions_for_cubic_lattice(N1, N2, N3)
-LDOS = gjh.local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2, N3=N3)
+LDOS = gjh.local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2, N3=N3)
-print('cubic lattice:\n', LDOS, '\n')
+print('cubic lattice:\n', LDOS, '\n')
-
+
-h00 = gjh.finite_size_along_two_directions_for_square_lattice(N2, N3)
+h00 = gjh.finite_size_along_two_directions_for_square_lattice(N2, N3)
-h01 = np.identity(N2*N3)
+h01 = np.identity(N2*N3)
-LDOS = gjh.local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3=N3, N2=N2, N1=N1)
+LDOS = gjh.local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3=N3, N2=N2, N1=N1)
 print(LDOS)

Tutorial/7_conductance.py

@@ -1,8 +1,8 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-
+
-fermi_energy_array = np.linspace(-5, 5, 400)
+fermi_energy_array = np.linspace(-5, 5, 400)
-h00 = gjh.finite_size_along_one_direction(4)
+h00 = gjh.finite_size_along_one_direction(4)
-h01 = np.identity(4)
+h01 = np.identity(4)
-conductance_array = gjh.calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01)
+conductance_array = gjh.calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01)
 gjh.plot(fermi_energy_array, conductance_array, xlabel='E', ylabel='Conductance', type='-o')

Tutorial/8_scattering_matrix.py

@@ -1,7 +1,7 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-
+
-fermi_energy = 0
+fermi_energy = 0
-h00 = gjh.finite_size_along_one_direction(4)
+h00 = gjh.finite_size_along_one_direction(4)
-h01 = np.identity(4)
+h01 = np.identity(4)
 gjh.print_or_write_scattering_matrix(fermi_energy, h00, h01)

Tutorial/9_Chern_number.py

@@ -1,18 +1,18 @@
-import gjh
+import gjh
-import numpy as np
+import numpy as np
-from math import *
+from math import *
-
+
-def hamiltonian_function(kx, ky):  # one QAH model with chern number 2
+def hamiltonian_function(kx, ky):  # one QAH model with chern number 2
-    t1 = 1.0
+    t1 = 1.0
-    t2 = 1.0
+    t2 = 1.0
-    t3 = 0.5
+    t3 = 0.5
-    m = -1.0
+    m = -1.0
-    hamiltonian = np.zeros((2, 2), dtype=complex)
+    hamiltonian = np.zeros((2, 2), dtype=complex)
-    hamiltonian[0, 1] = 2*t1*cos(kx)-1j*2*t1*cos(ky)
+    hamiltonian[0, 1] = 2*t1*cos(kx)-1j*2*t1*cos(ky)
-    hamiltonian[1, 0] = 2*t1*cos(kx)+1j*2*t1*cos(ky)
+    hamiltonian[1, 0] = 2*t1*cos(kx)+1j*2*t1*cos(ky)
-    hamiltonian[0, 0] = m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky)
+    hamiltonian[0, 0] = m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky)
-    hamiltonian[1, 1] = -(m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky))
+    hamiltonian[1, 1] = -(m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky))
-    return hamiltonian
+    return hamiltonian
-
+
-chern_number = gjh.calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100)
+chern_number = gjh.calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100)
 print(chern_number)