update

2022.11.06_band_folding/band_folding.py

@@ -0,0 +1,30 @@
+"""
+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/27656
+"""
+
+import guan
+import numpy as np
+
+# one dimensional chain model
+unit_cell = 0
+hopping = 1
+hamiltonian_function = guan.one_dimensional_fourier_transform_with_k(unit_cell, hopping)
+k_array = np.linspace(-np.pi, np.pi, 100)
+eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
+guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='k', title='one dimensional chain model')
+
+# n times band folding
+max_n = 10
+for n in np.arange(2, max_n+1):
+    unit_cell = np.zeros((n, n))
+    for i0 in range(int(n)):
+        for j0 in range(int(n)):
+            if abs(i0-j0)==1:
+                unit_cell[i0, j0] = 1
+    hopping = np.zeros((n, n))
+    hopping[0, n-1] = 1
+    hamiltonian_function = guan.one_dimensional_fourier_transform_with_k(unit_cell, hopping)
+    k_array = np.linspace(-np.pi, np.pi, 100)
+    eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
+    guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='k', title='%i times band folding'%n)