update

2020.09.29_Halmiltonian_and_Fermi_arc_in_Weyl_semimetals/Fermi_arc_in_Weyl_semimetals.py

@@ -0,0 +1,64 @@
+"""
+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/6077
+"""
+
+import numpy as np
+from math import *
+import matplotlib.pyplot as plt
+
+
+def main():
+    n =  0.5
+    k1 = np.arange(-n*pi, n*pi, n/50)
+    k2 = np.arange(-n*pi, n*pi, n/50)
+    plot_bands_two_dimension_direct(k1, k2, hamiltonian)
+
+
+def hamiltonian(kx,kz,ky=0):  # surface states of Weyl semimetal
+    A = 1
+    H = A*kx
+    return H
+
+
+def sigma_x():
+    return np.array([[0, 1],[1, 0]])
+
+
+def sigma_y():
+    return np.array([[0, -1j],[1j, 0]])
+
+
+def sigma_z():
+    return np.array([[1, 0],[0, -1]])
+
+
+def plot_bands_two_dimension_direct(k1, k2, hamiltonian):
+    from mpl_toolkits.mplot3d import Axes3D
+    from matplotlib import cm
+    from matplotlib.ticker import LinearLocator, FormatStrFormatter
+    fig = plt.figure()
+    ax = fig.gca(projection='3d')
+    dim1 = k1.shape[0]
+    dim2 = k2.shape[0]
+    eigenvalue_k = np.zeros((dim2, dim1))
+    i0 = 0   
+    for k10 in k1:
+        j0 = 0
+        for k20 in k2:
+            if (k10**2+k20**2 <= 1):
+                eigenvalue_k[j0, i0] = hamiltonian(k10, k20)
+            else:
+                eigenvalue_k[j0, i0] = 'nan'
+            j0 += 1
+        i0 += 1
+    k1, k2 = np.meshgrid(k1, k2)
+    ax.scatter(k1, k2, eigenvalue_k)
+    plt.xlabel('kx')
+    plt.ylabel('kz')
+    ax.set_zlabel('E')  
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()

2020.09.29_Halmiltonian_and_Fermi_arc_in_Weyl_semimetals/bands_of_Weyl_semimetals.py

@@ -0,0 +1,67 @@
+"""
+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/6077
+"""
+
+import numpy as np
+from math import *
+import matplotlib.pyplot as plt
+
+
+def main():
+    n =  0.5
+    k1 = np.arange(-n*pi, n*pi, n/20)
+    k2 = np.arange(-n*pi, n*pi, n/20)
+    plot_bands_two_dimension(k1, k2, hamiltonian)
+
+
+def hamiltonian(kx,kz,ky=0):  # Weyl semimetal
+    A = 1
+    M0 = 1
+    M1 = 1
+    H = A*(kx*sigma_x()+ky*sigma_y())+(M0-M1*(kx**2+ky**2+kz**2))*sigma_z()
+    return H
+
+
+def sigma_x():
+    return np.array([[0, 1],[1, 0]])
+
+
+def sigma_y():
+    return np.array([[0, -1j],[1j, 0]])
+
+
+def sigma_z():
+    return np.array([[1, 0],[0, -1]])
+
+
+def plot_bands_two_dimension(k1, k2, hamiltonian):
+    from mpl_toolkits.mplot3d import Axes3D
+    from matplotlib import cm
+    from matplotlib.ticker import LinearLocator, FormatStrFormatter
+    dim = hamiltonian(0, 0).shape[0]
+    dim1 = k1.shape[0]
+    dim2 = k2.shape[0]
+    eigenvalue_k = np.zeros((dim2, dim1, dim))
+    i0 = 0
+    for k10 in k1:
+        j0 = 0
+        for k20 in k2:
+            matrix0 = hamiltonian(k10, k20)
+            eigenvalue, eigenvector = np.linalg.eig(matrix0)
+            eigenvalue_k[j0, i0, :] = np.sort(np.real(eigenvalue[:]))
+            j0 += 1
+        i0 += 1
+    fig = plt.figure()
+    ax = fig.gca(projection='3d')
+    k1, k2 = np.meshgrid(k1, k2)
+    for dim0 in range(dim):
+        ax.plot_surface(k1, k2, eigenvalue_k[:, :, dim0], cmap=cm.coolwarm, linewidth=0, antialiased=False)
+    plt.xlabel('kx')
+    plt.ylabel('kz') 
+    ax.set_zlabel('E')  
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()