163 lines
6.9 KiB
Python
163 lines
6.9 KiB
Python
"""
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This code is supported by the website: https://www.guanjihuan.com
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The newest version of this code is on the web page: https://www.guanjihuan.com/archives/17984
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"""
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import numpy as np
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import cmath
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from math import *
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import functools
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def hamiltonian(kx, ky): # BBH model
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# label of atoms in a unit cell
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# (2) —— (0)
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# | |
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# (1) —— (3)
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gamma_x = 0.5 # hopping inside one unit cell
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lambda_x = 1 # hopping between unit cells
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gamma_y = gamma_x
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lambda_y = lambda_x
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h = np.zeros((4, 4), dtype=complex)
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h[0, 2] = gamma_x+lambda_x*cmath.exp(1j*kx)
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h[1, 3] = gamma_x+lambda_x*cmath.exp(-1j*kx)
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h[0, 3] = gamma_y+lambda_y*cmath.exp(1j*ky)
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h[1, 2] = -gamma_y-lambda_y*cmath.exp(-1j*ky)
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h[2, 0] = np.conj(h[0, 2])
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h[3, 1] = np.conj(h[1, 3])
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h[3, 0] = np.conj(h[0, 3])
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h[2, 1] = np.conj(h[1, 2])
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return h
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def main():
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kx = np.arange(-pi, pi, 0.05)
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ky = np.arange(-pi, pi, 0.05)
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eigenvalue_array = calculate_eigenvalue_with_two_parameters(kx, ky, hamiltonian)
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plot_3d_surface(kx, ky, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E', title='BBH bands')
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hamiltonian0 = functools.partial(hamiltonian, ky=0)
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eigenvalue_array = calculate_eigenvalue_with_one_parameter(kx, hamiltonian0)
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plot(kx, eigenvalue_array, xlabel='kx', ylabel='E', title='BBH bands ky=0')
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# import guan
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# eigenvalue_array = guan.calculate_eigenvalue_with_two_parameters(kx, ky, hamiltonian)
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# guan.plot_3d_surface(kx, ky, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E', title='BBH bands')
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# hamiltonian0 = functools.partial(hamiltonian, ky=0)
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# eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(kx, hamiltonian0)
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# guan.plot(kx, eigenvalue_array, xlabel='kx', ylabel='E', title='BBH bands ky=0')
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def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0):
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dim_x = np.array(x_array).shape[0]
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i0 = 0
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if np.array(hamiltonian_function(0)).shape==():
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eigenvalue_array = np.zeros((dim_x, 1))
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for x0 in x_array:
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hamiltonian = hamiltonian_function(x0)
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eigenvalue_array[i0, 0] = np.real(hamiltonian)
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i0 += 1
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else:
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dim = np.array(hamiltonian_function(0)).shape[0]
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eigenvalue_array = np.zeros((dim_x, dim))
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for x0 in x_array:
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if print_show==1:
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print(x0)
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hamiltonian = hamiltonian_function(x0)
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eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
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eigenvalue_array[i0, :] = eigenvalue
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i0 += 1
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return eigenvalue_array
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def calculate_eigenvalue_with_two_parameters(x_array, y_array, hamiltonian_function, print_show=0, print_show_more=0):
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dim_x = np.array(x_array).shape[0]
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dim_y = np.array(y_array).shape[0]
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if np.array(hamiltonian_function(0,0)).shape==():
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eigenvalue_array = np.zeros((dim_y, dim_x, 1))
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i0 = 0
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for y0 in y_array:
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j0 = 0
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for x0 in x_array:
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hamiltonian = hamiltonian_function(x0, y0)
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eigenvalue_array[i0, j0, 0] = np.real(hamiltonian)
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j0 += 1
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i0 += 1
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else:
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dim = np.array(hamiltonian_function(0, 0)).shape[0]
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eigenvalue_array = np.zeros((dim_y, dim_x, dim))
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i0 = 0
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for y0 in y_array:
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j0 = 0
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if print_show==1:
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print(y0)
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for x0 in x_array:
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if print_show_more==1:
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print(x0)
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hamiltonian = hamiltonian_function(x0, y0)
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eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
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eigenvalue_array[i0, j0, :] = eigenvalue
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j0 += 1
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i0 += 1
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return eigenvalue_array
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def plot(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style='', y_min=None, y_max=None, linewidth=None, markersize=None, adjust_bottom=0.2, adjust_left=0.2):
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import matplotlib.pyplot as plt
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fig, ax = plt.subplots()
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plt.subplots_adjust(bottom=adjust_bottom, left=adjust_left)
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ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize)
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ax.grid()
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ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
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ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
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ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
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if y_min!=None or y_max!=None:
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if y_min==None:
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y_min=min(y_array)
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if y_max==None:
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y_max=max(y_array)
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ax.set_ylim(y_min, y_max)
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ax.tick_params(labelsize=labelsize)
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labels = ax.get_xticklabels() + ax.get_yticklabels()
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[label.set_fontname('Times New Roman') for label in labels]
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if save == 1:
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plt.savefig(filename+file_format, dpi=dpi)
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if show == 1:
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plt.show()
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plt.close('all')
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def plot_3d_surface(x_array, y_array, matrix, xlabel='x', ylabel='y', zlabel='z', title='', fontsize=20, labelsize=15, show=1, save=0, filename='a', file_format='.jpg', dpi=300, z_min=None, z_max=None, rcount=100, ccount=100):
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import matplotlib.pyplot as plt
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from matplotlib import cm
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from matplotlib.ticker import LinearLocator
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matrix = np.array(matrix)
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fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
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plt.subplots_adjust(bottom=0.1, right=0.65)
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x_array, y_array = np.meshgrid(x_array, y_array)
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if len(matrix.shape) == 2:
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surf = ax.plot_surface(x_array, y_array, matrix, rcount=rcount, ccount=ccount, cmap=cm.coolwarm, linewidth=0, antialiased=False)
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elif len(matrix.shape) == 3:
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for i0 in range(matrix.shape[2]):
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surf = ax.plot_surface(x_array, y_array, matrix[:,:,i0], rcount=rcount, ccount=ccount, cmap=cm.coolwarm, linewidth=0, antialiased=False)
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ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
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ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
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ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
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ax.set_zlabel(zlabel, fontsize=fontsize, fontfamily='Times New Roman')
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ax.zaxis.set_major_locator(LinearLocator(5))
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ax.zaxis.set_major_formatter('{x:.2f}')
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if z_min!=None or z_max!=None:
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if z_min==None:
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z_min=matrix.min()
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if z_max==None:
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z_max=matrix.max()
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ax.set_zlim(z_min, z_max)
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ax.tick_params(labelsize=labelsize)
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labels = ax.get_xticklabels() + ax.get_yticklabels() + ax.get_zticklabels()
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[label.set_fontname('Times New Roman') for label in labels]
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cax = plt.axes([0.8, 0.1, 0.05, 0.8])
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cbar = fig.colorbar(surf, cax=cax)
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cbar.ax.tick_params(labelsize=labelsize)
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for l in cbar.ax.yaxis.get_ticklabels():
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l.set_family('Times New Roman')
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if save == 1:
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plt.savefig(filename+file_format, dpi=dpi)
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if show == 1:
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plt.show()
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plt.close('all')
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if __name__ == '__main__':
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main() |