Band calc. - Tri. lattice

gitrymt · gitrymt · commit b0cd432ff691 · 2018-02-16T01:10:01.000+09:00
diff --git a/Calculation/.spyproject/workspace.ini b/Calculation/.spyproject/workspace.ini
@@ -6,5 +6,5 @@ save_non_project_files = False
 
 [main]
 version = 0.1.0
-recent_files = ['C:\\GitHub\\python\\Calculation\\example\\band_calc_1d.py', 'C:\\GitHub\\python\\Calculation\\example\\band_gap_1d.py', 'C:\\GitHub\\python\\Calculation\\example\\Wannier_function_1d.py', 'C:\\GitHub\\python\\Calculation\\example\\band_calc_2d.py']
+recent_files = ['C:\\GitHub\\python\\Calculation\\example\\band_calc_1d.py', 'C:\\GitHub\\python\\Calculation\\example\\band_gap_1d.py', 'C:\\GitHub\\python\\Calculation\\example\\Wannier_function_1d.py', 'C:\\GitHub\\python\\Calculation\\example\\band_calc_2d.py', 'C:\\GitHub\\python\\Calculation\\example\\band_calc_tri.py']
 
diff --git a/Calculation/example/band_calc_tri.py b/Calculation/example/band_calc_tri.py
@@ -0,0 +1,109 @@
+# -*- coding: utf-8 -*-
+"""
+Example for calculation of band structure: Triangular optical lattice
+
+Created on Thu Feb 15 20:37:38 2018
+@author: gitrymt
+"""
+import sys
+import numpy as np
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import axes3d
+from matplotlib import cm
+import pandas as pd
+
+# import user library
+sys.path.append('../function')
+#from func_band_calc import calcBand_1d
+
+# Lattice depth V_lat = s Er
+s = 1
+
+# Calculation
+m = 6
+Nsite = 2 * m + 1
+
+b1 = np.array([1, 0])
+b2 = np.array([-1, -np.sqrt(3)])/2
+b3 = np.array([-1, np.sqrt(3)])/2
+
+p_Gamma = 0 * b1 + 0 * b2
+p_M = 1/2 * b1 + 0 * b2
+p_K = 1/3 * b1 - 1/3 * b2
+fig = plt.figure()
+ax = fig.add_subplot(111)
+# 5点(0.1,0.1),(0.1,0.6),(0.7,0.8),(0.6,0.4),(0.6,0.1)を通る多角形を描画
+poly = plt.Polygon((p_Gamma, p_M, p_K, p_Gamma),fc="#ff0000", alpha=0.5)
+ax.add_patch(poly)
+plt.show()
+
+
+dn = 25
+
+n_list = [(x, 0) for x in np.linspace(0, 1/2, int(dn * np.sqrt(3)))] # Gamma -> M
+n_M = len(n_list) - 0.5
+
+n_list = n_list + [(1/2 - x/6, -x/3) for x in np.linspace(0, 1, dn) if x>0] # M -> K
+#n_K = len([(0.5, -x) for x in np.linspace(0, 1/3, dn)])
+n_K = len(n_list) - 0.5
+
+n_list = n_list + [(x/3, -x/3) for x in np.linspace(1, 0, dn*2) if x<1] # K -> Gamma
+#n_Gamma = len([(x, -x) for x in np.linspace(1/3, 0, dn*2)])
+n_Gamma = len(n_list)
+
+l_list = [(x, y) for x in np.linspace(-m, m, Nsite) for y in np.linspace(-m, m, Nsite)]
+E = np.zeros([len(n_list), Nsite**2])
+
+list_emp = []
+condition = pd.DataFrame([[list_emp, list_emp, list_emp,
+                           False, False, False]],
+                        columns = ["(l1, l2)", "(l1', l2')", "(l1-l1', l2-l2')",
+                                   "Condition 1", "Condition 2", "Condition 3"
+                                   ])
+
+for i_n, n in enumerate(n_list):
+    H = np.zeros([Nsite**2, Nsite**2])
+    
+    for i_1, ls_1 in enumerate(l_list):
+        for i_2, ls_2 in enumerate(l_list):
+            l_diff = np.array(ls_1) - np.array(ls_2)
+            
+            if (ls_1[0] == ls_2[0]) and (ls_1[1] == ls_2[1]):
+                H[i_1][i_2] = 3 * ((n[0] + ls_1[0])**2 + (n[1] + ls_1[1])**2 - (n[0] + ls_1[0]) * (n[1] + ls_1[1])) - 3 * s / 4
+            
+#            if ((np.abs(ls_1[0] - ls_2[0]) == 1) and (ls_1[1] == ls_2[1])\
+#                or ((ls_1[0] == ls_2[0]) and np.abs(ls_1[1] - ls_2[1]) == 1)\
+#                or ((ls_1[0] - ls_2[0] == ls_1[1] - ls_2[1]) and (np.abs(ls_1[1] - ls_2[1]) == 1))):
+            
+            
+            condition_1 = (int(np.abs(ls_1[0] - ls_2[0])) == 1) and (ls_1[1] == ls_2[1])
+            condition_2 = (ls_1[0] == ls_2[0]) and (int(np.abs(ls_1[1] - ls_2[1])) == 1)
+#            condition_3 = (int(ls_1[0] - ls_1[1]) == int(ls_2[0] - ls_2[1])) and (int(np.abs(ls_2[0] - ls_2[1])) == 1)
+            condition_3 = ((l_diff[0] == 1) and (l_diff[1] == 1)) or ((l_diff[0] == -1) and (l_diff[1] == -1))
+#            condition_1 = (np.abs(l_diff[0] == 1)) and (ls_1[1] == ls_2[1])
+#            condition_2 = (np.abs(l_diff[1] == 1)) and (ls_1[0] == ls_2[0])
+#            condition_3 = (l_diff[0] * l_diff[1]) == -1
+            if condition_1 or condition_2 or condition_3:
+                H[i_1][i_2] = - s / 4
+                
+                tmp = pd.DataFrame([[ls_1, ls_2, l_diff,
+                                     condition_1, condition_2, condition_3]],
+                            columns = ["(l1, l2)", "(l1', l2')", "(l1-l1', l2-l2')",
+                                       "Condition 1", "Condition 2", "Condition 3"
+                                       ])
+                condition = condition.append(tmp)
+            
+    E0, P = np.linalg.eig(H)
+    rearrangedEvalsVecs = sorted(zip(E0, P.T), key=lambda x: x[0].real, reverse=False)
+    
+    for i in range(Nsite**2):
+        E[i_n, i] = rearrangedEvalsVecs[i][0]
+#        P[:, i] = rearrangedEvalsVecs[i][1]
+
+
+q = np.linspace(0, len(n_list), len(n_list))
+plt.figure(dpi=200)
+plt.plot(q, E[:, 0:4] - E[0, 0])
+plt.grid(ls=':')
+plt.ylabel('Energy ($E_R$)')
+plt.xticks([0, n_M, n_K, n_Gamma], ['$\Gamma$', 'M', 'K', '$\Gamma$']) # xlocs：位置の配列　xlabels：ラベルの配列
