From 1fc6f55a5a2cc197de37055820d1d010a8d05255 Mon Sep 17 00:00:00 2001 From: guanjihuan Date: Sun, 28 Aug 2022 02:35:57 +0800 Subject: [PATCH] Create Berry_curvature_distribution_with_the_efficient_method_for_degenerate_case_(function_form).py --- ...hod_for_degenerate_case_(function_form).py | 183 ++++++++++++++++++ 1 file changed, 183 insertions(+) create mode 100644 academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_the_efficient_method_for_degenerate_case_(function_form).py diff --git a/academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_the_efficient_method_for_degenerate_case_(function_form).py b/academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_the_efficient_method_for_degenerate_case_(function_form).py new file mode 100644 index 0000000..1fce9e6 --- /dev/null +++ b/academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_the_efficient_method_for_degenerate_case_(function_form).py @@ -0,0 +1,183 @@ +""" +This code is supported by the website: https://www.guanjihuan.com +The newest version of this code is on the web page: https://www.guanjihuan.com/archives/24059 +""" + +import numpy as np +from math import * +import cmath +import math + + +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)） + h = np.zeros((2, 2))*(1+0j) + h[0, 0] = 0.28/2 + h[1, 1] = -0.28/2 + 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)) + h[0, 1] = h[1, 0].conj() + return h + + +def main(): + 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) + dim = berry_curvature_array.shape + plot_3d_surface(k_array, k_array, np.real(berry_curvature_array), title='Valence Band', xlabel='kx', ylabel='ky', zlabel='Berry curvature') + plot(k_array, np.real(berry_curvature_array[int(dim[0]/2), :]), title='Valence Band ky=0', xlabel='kx', ylabel='Berry curvature') # ky=0 + + 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) + dim = berry_curvature_array.shape + plot_3d_surface(k_array, k_array, np.real(berry_curvature_array), title='All Band', xlabel='kx', ylabel='ky', zlabel='Berry curvature') + plot(k_array, np.real(berry_curvature_array[int(dim[0]/2), :]), title='All Band ky=0', xlabel='kx', ylabel='Berry curvature') # ky=0 + + + # import guan + # 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) + # dim = berry_curvature_array.shape + # guan.plot_3d_surface(k_array, k_array, np.real(berry_curvature_array), title='Valence Band', xlabel='kx', ylabel='ky', zlabel='Berry curvature') + # 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 + + # 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) + # dim = berry_curvature_array.shape + # guan.plot_3d_surface(k_array, k_array, np.real(berry_curvature_array), title='All Band', xlabel='kx', ylabel='ky', zlabel='Berry curvature') + # 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 + + + +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): + delta = (k_max-k_min)/precision + k_array = np.arange(k_min, k_max, delta) + berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0]), dtype=complex) + i00 = 0 + for kx in np.arange(k_min, k_max, delta): + if print_show == 1: + print(kx) + j00 = 0 + for ky in np.arange(k_min, k_max, delta): + H = hamiltonian_function(kx, ky) + eigenvalue, vector = np.linalg.eigh(H) + H_delta_kx = hamiltonian_function(kx+delta, ky) + eigenvalue, vector_delta_kx = np.linalg.eigh(H_delta_kx) + H_delta_ky = hamiltonian_function(kx, ky+delta) + eigenvalue, vector_delta_ky = np.linalg.eigh(H_delta_ky) + H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta) + eigenvalue, vector_delta_kx_ky = np.linalg.eigh(H_delta_kx_ky) + dim = len(index_of_bands) + det_value = 1 + # first dot + dot_matrix = np.zeros((dim , dim), dtype=complex) + i0 = 0 + for dim1 in index_of_bands: + j0 = 0 + for dim2 in index_of_bands: + dot_matrix[dim1, dim2] = np.dot(np.conj(vector[:, dim1]), vector_delta_kx[:, dim2]) + j0 += 1 + i0 += 1 + dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix)) + det_value = det_value*dot_matrix + # second dot + dot_matrix = np.zeros((dim , dim), dtype=complex) + i0 = 0 + for dim1 in index_of_bands: + j0 = 0 + for dim2 in index_of_bands: + dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_kx[:, dim1]), vector_delta_kx_ky[:, dim2]) + j0 += 1 + i0 += 1 + dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix)) + det_value = det_value*dot_matrix + # third dot + dot_matrix = np.zeros((dim , dim), dtype=complex) + i0 = 0 + for dim1 in index_of_bands: + j0 = 0 + for dim2 in index_of_bands: + dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_kx_ky[:, dim1]), vector_delta_ky[:, dim2]) + j0 += 1 + i0 += 1 + dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix)) + det_value = det_value*dot_matrix + # four dot + dot_matrix = np.zeros((dim , dim), dtype=complex) + i0 = 0 + for dim1 in index_of_bands: + j0 = 0 + for dim2 in index_of_bands: + dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_ky[:, dim1]), vector[:, dim2]) + j0 += 1 + i0 += 1 + dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix)) + det_value= det_value*dot_matrix + berry_curvature = cmath.log(det_value)/delta/delta*1j + berry_curvature_array[j00, i00] = berry_curvature + j00 += 1 + i00 += 1 + return k_array, berry_curvature_array + + +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): + import matplotlib.pyplot as plt + from matplotlib import cm + from matplotlib.ticker import LinearLocator + matrix = np.array(matrix) + fig, ax = plt.subplots(subplot_kw={"projection": "3d"}) + plt.subplots_adjust(bottom=0.1, right=0.65) + x_array, y_array = np.meshgrid(x_array, y_array) + if len(matrix.shape) == 2: + surf = ax.plot_surface(x_array, y_array, matrix, rcount=rcount, ccount=ccount, cmap=cm.coolwarm, linewidth=0, antialiased=False) + elif len(matrix.shape) == 3: + for i0 in range(matrix.shape[2]): + surf = ax.plot_surface(x_array, y_array, matrix[:,:,i0], rcount=rcount, ccount=ccount, cmap=cm.coolwarm, linewidth=0, antialiased=False) + ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman') + ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman') + ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman') + ax.set_zlabel(zlabel, fontsize=fontsize, fontfamily='Times New Roman') + ax.zaxis.set_major_locator(LinearLocator(5)) + ax.zaxis.set_major_formatter('{x:.2f}') + if z_min!=None or z_max!=None: + if z_min==None: + z_min=matrix.min() + if z_max==None: + z_max=matrix.max() + ax.set_zlim(z_min, z_max) + ax.tick_params(labelsize=labelsize) + labels = ax.get_xticklabels() + ax.get_yticklabels() + ax.get_zticklabels() + [label.set_fontname('Times New Roman') for label in labels] + cax = plt.axes([0.8, 0.1, 0.05, 0.8]) + cbar = fig.colorbar(surf, cax=cax) + cbar.ax.tick_params(labelsize=labelsize) + for l in cbar.ax.yaxis.get_ticklabels(): + l.set_family('Times New Roman') + if save == 1: + plt.savefig(filename+'.'+format, dpi=dpi) + if show == 1: + plt.show() + plt.close('all') + + +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): + import matplotlib.pyplot as plt + fig, ax = plt.subplots() + plt.subplots_adjust(bottom=adjust_bottom, left=adjust_left) + ax.grid() + ax.tick_params(labelsize=labelsize) + labels = ax.get_xticklabels() + ax.get_yticklabels() + [label.set_fontname('Times New Roman') for label in labels] + ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize) + ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman') + ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman') + ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman') + if y_min!=None or y_max!=None: + if y_min==None: + y_min=min(y_array) + if y_max==None: + y_max=max(y_array) + ax.set_ylim(y_min, y_max) + if save == 1: + plt.savefig(filename+'.'+format, dpi=dpi) + if show == 1: + plt.show() + plt.close('all') + + +if __name__ == '__main__': + main() \ No newline at end of file