103 lines
4.2 KiB
Python
103 lines
4.2 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/16730
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"""
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import numpy as np
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from math import *
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def hamiltonian(kx, ky): # kagome lattice
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k1_dot_a1 = kx
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k2_dot_a2 = kx/2+ky*sqrt(3)/2
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k3_dot_a3 = -kx/2+ky*sqrt(3)/2
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h = np.zeros((3, 3), dtype=complex)
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h[0, 1] = 2*cos(k1_dot_a1)
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h[0, 2] = 2*cos(k2_dot_a2)
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h[1, 2] = 2*cos(k3_dot_a3)
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h = h + h.transpose().conj()
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t = 1
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h = -t*h
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return h
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def main():
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kx_array = np.linspace(-pi ,pi, 500)
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ky_array = np.linspace(-pi ,pi, 500)
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eigenvalue_array = calculate_eigenvalue_with_two_parameters(kx_array, ky_array, hamiltonian)
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plot_3d_surface(kx_array, ky_array, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E', rcount=200, ccount=200)
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# import guan
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# eigenvalue_array = guan.calculate_eigenvalue_with_two_parameters(kx_array, ky_array, hamiltonian)
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# guan.plot_3d_surface(kx_array, ky_array, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E', rcount=200, ccount=200)
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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_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() |