Create Berry_curvature_distribution_with_the_efficient_method_for_degenerate_case_(function_form).py
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"""
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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/24059
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"""
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import numpy as np
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from math import *
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import cmath
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import math
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def hamiltonian(k1, k2, t1=2.82, a=1/sqrt(3)): # 石墨烯哈密顿量（a为原子间距，不赋值的话默认为1/sqrt(3)）
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h = np.zeros((2, 2))*(1+0j)
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h[0, 0] = 0.28/2
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h[1, 1] = -0.28/2
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h[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a))
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h[0, 1] = h[1, 0].conj()
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return h
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def main():
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k_array, berry_curvature_array = calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function=hamiltonian, index_of_bands=[0], k_min=-2*math.pi, k_max=2*math.pi, precision=500)
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dim = berry_curvature_array.shape
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plot_3d_surface(k_array, k_array, np.real(berry_curvature_array), title='Valence Band', xlabel='kx', ylabel='ky', zlabel='Berry curvature')
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plot(k_array, np.real(berry_curvature_array[int(dim[0]/2), :]), title='Valence Band ky=0', xlabel='kx', ylabel='Berry curvature') # ky=0
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k_array, berry_curvature_array = calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function=hamiltonian, index_of_bands=[0, 1], k_min=-2*math.pi, k_max=2*math.pi, precision=500)
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dim = berry_curvature_array.shape
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plot_3d_surface(k_array, k_array, np.real(berry_curvature_array), title='All Band', xlabel='kx', ylabel='ky', zlabel='Berry curvature')
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plot(k_array, np.real(berry_curvature_array[int(dim[0]/2), :]), title='All Band ky=0', xlabel='kx', ylabel='Berry curvature') # ky=0
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# import guan
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# k_array, berry_curvature_array = guan.calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function=hamiltonian, index_of_bands=[0], k_min=-2*math.pi, k_max=2*math.pi, precision=500)
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# dim = berry_curvature_array.shape
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# guan.plot_3d_surface(k_array, k_array, np.real(berry_curvature_array), title='Valence Band', xlabel='kx', ylabel='ky', zlabel='Berry curvature')
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# guan.plot(k_array, np.real(berry_curvature_array[int(dim[0]/2), :]), title='Valence Band ky=0', xlabel='kx', ylabel='Berry curvature') # ky=0
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# k_array, berry_curvature_array = guan.calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function=hamiltonian, index_of_bands=[0, 1], k_min=-2*math.pi, k_max=2*math.pi, precision=500)
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# dim = berry_curvature_array.shape
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# guan.plot_3d_surface(k_array, k_array, np.real(berry_curvature_array), title='All Band', xlabel='kx', ylabel='ky', zlabel='Berry curvature')
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# guan.plot(k_array, np.real(berry_curvature_array[int(dim[0]/2), :]), title='All Band ky=0', xlabel='kx', ylabel='Berry curvature') # ky=0
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def calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min=-math.pi, k_max=math.pi, precision=100, print_show=0):
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delta = (k_max-k_min)/precision
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k_array = np.arange(k_min, k_max, delta)
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berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0]), dtype=complex)
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i00 = 0
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for kx in np.arange(k_min, k_max, delta):
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if print_show == 1:
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print(kx)
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j00 = 0
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for ky in np.arange(k_min, k_max, delta):
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H = hamiltonian_function(kx, ky)
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eigenvalue, vector = np.linalg.eigh(H)
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H_delta_kx = hamiltonian_function(kx+delta, ky)
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eigenvalue, vector_delta_kx = np.linalg.eigh(H_delta_kx)
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H_delta_ky = hamiltonian_function(kx, ky+delta)
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eigenvalue, vector_delta_ky = np.linalg.eigh(H_delta_ky)
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H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
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eigenvalue, vector_delta_kx_ky = np.linalg.eigh(H_delta_kx_ky)
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dim = len(index_of_bands)
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det_value = 1
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# first dot
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dot_matrix = np.zeros((dim , dim), dtype=complex)
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i0 = 0
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for dim1 in index_of_bands:
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j0 = 0
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for dim2 in index_of_bands:
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dot_matrix[dim1, dim2] = np.dot(np.conj(vector[:, dim1]), vector_delta_kx[:, dim2])
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j0 += 1
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i0 += 1
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dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
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det_value = det_value*dot_matrix
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# second dot
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dot_matrix = np.zeros((dim , dim), dtype=complex)
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i0 = 0
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for dim1 in index_of_bands:
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j0 = 0
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for dim2 in index_of_bands:
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dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_kx[:, dim1]), vector_delta_kx_ky[:, dim2])
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j0 += 1
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i0 += 1
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dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
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det_value = det_value*dot_matrix
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# third dot
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dot_matrix = np.zeros((dim , dim), dtype=complex)
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i0 = 0
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for dim1 in index_of_bands:
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j0 = 0
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for dim2 in index_of_bands:
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dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_kx_ky[:, dim1]), vector_delta_ky[:, dim2])
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j0 += 1
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i0 += 1
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dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
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det_value = det_value*dot_matrix
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# four dot
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dot_matrix = np.zeros((dim , dim), dtype=complex)
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i0 = 0
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for dim1 in index_of_bands:
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j0 = 0
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for dim2 in index_of_bands:
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dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_ky[:, dim1]), vector[:, dim2])
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j0 += 1
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i0 += 1
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dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
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det_value= det_value*dot_matrix
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berry_curvature = cmath.log(det_value)/delta/delta*1j
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berry_curvature_array[j00, i00] = berry_curvature
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j00 += 1
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i00 += 1
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return k_array, berry_curvature_array
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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', 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+'.'+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(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', 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.grid()
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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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ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize)
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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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if save == 1:
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plt.savefig(filename+'.'+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()
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