update

2023-11-07 03:38:46 +08:00
parent 1e7c4c0e68
commit bc3890c25b
212 changed files with 0 additions and 0 deletions
--- a/2021.08.09_flat_bands_of_Kagome
+++ b/2021.08.09_flat_bands_of_Kagome
@@ -0,0 +1,90 @@
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--- a/2021.08.09_flat_bands_of_Kagome
+++ b/2021.08.09_flat_bands_of_Kagome
@@ -0,0 +1,103 @@
+"""
+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/16730
+"""
+
+import numpy as np
+from math import *
+
+def hamiltonian(kx, ky):  # kagome lattice
+    k1_dot_a1 = kx
+    k2_dot_a2 = kx/2+ky*sqrt(3)/2
+    k3_dot_a3 = -kx/2+ky*sqrt(3)/2
+    h = np.zeros((3, 3), dtype=complex)
+    h[0, 1] = 2*cos(k1_dot_a1)
+    h[0, 2] = 2*cos(k2_dot_a2)
+    h[1, 2] = 2*cos(k3_dot_a3)
+    h = h + h.transpose().conj()
+    t = 1
+    h = -t*h
+    return h
+
+def main():
+    kx_array = np.linspace(-pi ,pi, 500)
+    ky_array = np.linspace(-pi ,pi, 500)
+    eigenvalue_array = calculate_eigenvalue_with_two_parameters(kx_array, ky_array, hamiltonian)
+    plot_3d_surface(kx_array, ky_array, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E', rcount=200, ccount=200)
+    
+    # import guan
+    # eigenvalue_array = guan.calculate_eigenvalue_with_two_parameters(kx_array, ky_array, hamiltonian)
+    # guan.plot_3d_surface(kx_array, ky_array, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E', rcount=200, ccount=200)
+
+def calculate_eigenvalue_with_two_parameters(x_array, y_array, hamiltonian_function, print_show=0, print_show_more=0):  
+    dim_x = np.array(x_array).shape[0]
+    dim_y = np.array(y_array).shape[0]
+    if np.array(hamiltonian_function(0,0)).shape==():
+        eigenvalue_array = np.zeros((dim_y, dim_x, 1))
+        i0 = 0
+        for y0 in y_array:
+            j0 = 0
+            for x0 in x_array:
+                hamiltonian = hamiltonian_function(x0, y0)
+                eigenvalue_array[i0, j0, 0] = np.real(hamiltonian)
+                j0 += 1
+            i0 += 1
+    else:
+        dim = np.array(hamiltonian_function(0, 0)).shape[0]
+        eigenvalue_array = np.zeros((dim_y, dim_x, dim))
+        i0 = 0
+        for y0 in y_array:
+            j0 = 0
+            if print_show==1:
+                print(y0)
+            for x0 in x_array:
+                if print_show_more==1:
+                    print(x0)
+                hamiltonian = hamiltonian_function(x0, y0)
+                eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
+                eigenvalue_array[i0, j0, :] = eigenvalue
+                j0 += 1
+            i0 += 1
+    return eigenvalue_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', file_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+file_format, dpi=dpi) 
+    if show == 1:
+        plt.show()
+    plt.close('all')
+
+if __name__ == '__main__':
+    main()