update

Tutorial0/Fourier_transform_and_calculate_band_structures.py.py

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+import guan
+import numpy as np
+import functools
+
+# Fourier transform / calculate band structures / plot figures
+x_array = np.linspace(-np.pi, np.pi, 100)
+hamiltonian_function = functools.partial(guan.one_dimensional_fourier_transform, unit_cell=0, hopping=1)
+eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function)
+guan.plot(x_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')

Tutorial0/Hamiltonian_of_finite_size_systems.py

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+import guan
+
+# Hamiltonian of finite size
+print(guan.finite_size_along_one_direction(3), '\n')
+print(guan.finite_size_along_two_directions_for_square_lattice(2, 2), '\n')
+print(guan.finite_size_along_three_directions_for_cubic_lattice(2, 2, 2), '\n')

Tutorial0/calculate_Chern_number_and_Wilson_loop.py

@@ -0,0 +1,24 @@
+import guan
+import numpy as np
+from math import *
+
+# calculate Chern number
+def hamiltonian_function(kx, ky):  # one QAH model with chern number 2
+    t1 = 1.0
+    t2 = 1.0
+    t3 = 0.5
+    m = -1.0
+    hamiltonian = np.zeros((2, 2), dtype=complex)
+    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[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))
+    return hamiltonian
+chern_number = guan.calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100)
+print('Chern number=', chern_number)
+
+# calculate Wilson loop
+wilson_loop_array = guan.calculate_wilson_loop(guan.hamiltonian_of_ssh_model)
+print('Wilson loop =', wilson_loop_array)
+p = np.log(wilson_loop_array)/2/pi/1j
+print('p =', p, '\n')

Tutorial0/calculate_conductance_and_scattering_matrix.py

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+import guan
+import numpy as np
+
+# calculate conductance
+fermi_energy_array = np.linspace(-5, 5, 400)
+h00 = guan.finite_size_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='-o')
+
+# calculate scattering matrix
+fermi_energy = 0
+h00 = guan.finite_size_along_one_direction(4)
+h01 = np.identity(4)
+guan.print_or_write_scattering_matrix(fermi_energy, h00, h01)

Tutorial0/calculate_density_of_states.py

@@ -0,0 +1,31 @@
+import guan
+import numpy as np
+
+# calculate density of states
+hamiltonian = guan.finite_size_along_two_directions_for_square_lattice(2,2)
+fermi_energy_array = np.linspace(-4, 4, 400)
+total_dos_array = guan.total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.1)
+guan.plot(fermi_energy_array, total_dos_array, xlabel='E', ylabel='Total DOS', type='-o')
+
+fermi_energy = 0
+N1 = 3
+N2 = 4
+hamiltonian = guan.finite_size_along_two_directions_for_square_lattice(N1,N2)
+LDOS = guan.local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2)
+print('square lattice:\n', LDOS, '\n')
+h00 = guan.finite_size_along_one_direction(N2)
+h01 = np.identity(N2)
+LDOS = guan.local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00=h00, h01=h01, N2=N2, N1=N1)
+print(LDOS, '\n\n')
+# guan.plot_contour(range(N1), range(N2), LDOS)
+
+N1 = 3
+N2 = 4
+N3 = 5
+hamiltonian = guan.finite_size_along_three_directions_for_cubic_lattice(N1, N2, N3)
+LDOS = guan.local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2, N3=N3)
+print('cubic lattice:\n', LDOS, '\n')
+h00 = guan.finite_size_along_two_directions_for_square_lattice(N2, N3)
+h01 = np.identity(N2*N3)
+LDOS = guan.local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3=N3, N2=N2, N1=N1)
+print(LDOS)

Tutorial0/read_and_write.py

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+import guan
+import numpy as np
+
+# read and write
+x_array = np.array([1, 2, 3])
+y_array = np.array([5, 6, 7])
+guan.write_one_dimensional_data(x_array, y_array, filename='one_dimensional_data')
+matrix = np.zeros((3, 3))
+matrix[0, 1] = 11
+guan.write_two_dimensional_data(x_array, y_array, matrix, filename='two_dimensional_data')
+x_read, y_read = guan.read_one_dimensional_data('one_dimensional_data')
+print(x_read, '\n')
+print(y_read, '\n\n')
+x_read, y_read, matrix_read = guan.read_two_dimensional_data('two_dimensional_data')
+print(x_read, '\n')
+print(y_read, '\n')
+print(matrix_read)

Tutorial0/some_models_in_the_reciprocal_space.py

@@ -0,0 +1,9 @@
+import guan
+import numpy as np
+
+# Hamiltonian of models in the reciprocal space / calculate band structures / plot figures
+x_array = np.linspace(-np.pi, np.pi, 100)
+eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(x_array, guan.hamiltonian_of_square_lattice_in_quasi_one_dimension)
+guan.plot(x_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')
+eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(x_array, guan.hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension)
+guan.plot(x_array, eigenvalue_array, xlabel='k', ylabel='E', type='-k')

Tutorial0/test_and_Pauli_matrix.py

@@ -0,0 +1,12 @@
+import guan
+
+# test
+print('test')
+guan.test()
+
+# Pauli matrix
+print('Pauli matrix')
+print('sigma_0:\n', guan.sigma_0(), '\n')
+print('sigma_x:\n', guan.sigma_x(), '\n')
+print('sigma_y:\n', guan.sigma_y(), '\n')
+print('sigma_z:\n', guan.sigma_z(), '\n')