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Twist_bilayer.py
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# -*- coding: utf-8 -*-
"""
Created on Mon Aug 19 10:56:29 2024
@author: 26526
"""
import numpy as np
import matplotlib.pyplot as plt
from math import pi
from band_ini import config as cf
sq7 = np.sqrt(7)
sq21 = np.sqrt(21)
L1 = np.array([1.5*sq7, -0.5*sq21])
L2 = np.array([1.5*sq7, 0.5*sq21])
class twist_FM_1():
def __init__(self, J1=3):
self.H =np.zeros((7,7), dtype=complex)
self.J1 = J1
self.D = -0.1
self.Jc = -0.2
self.A0 = 0.5
#tilting term
self.tt = -0.5
#Haldane flux term
self.fk = self.D*1.j
self.fk_c = -self.D*1.j
def H11_11(self, k):
#H11_11 1st
H =np.zeros((7,7), dtype=complex)
H[0,1] = self.J1
H[1,0] = self.J1
H[0,5] = self.J1*np.exp(-1.j*k.dot(L1))
H[5,0] = H[0,5].conj()
H[1,2] = self.J1
H[2,1] = self.J1
H[2,2] = -self.Jc
H[2,3] = self.J1
H[3,2] = self.J1
H[3,4] = self.J1
H[4,3] = self.J1
H[4,5] = self.J1
H[5,4] = self.J1
H[5,6] = self.J1
H[6,5] = self.J1
#2nd
H[0,2] = self.fk
H[2,0] = H[0,2].conj()
H[0,4] = self.fk_c*np.exp(-1.j*k.dot(L1))
H[4,0] = H[0,4].conj()
H[0,6] = self.fk*np.exp(-1.j*k.dot(L1))
H[6,0] = H[0,6].conj()
H[1,3] = self.fk
H[3,1] = H[1,3].conj()
H[1,5] = self.fk*np.exp(-1.j*k.dot(L1))
H[5,1] = H[1,5].conj()
H[2,4] = self.fk_c
H[4,2] = H[2,4].conj()
H[2,6] = self.fk
H[6,2] = H[6,2].conj()
H[3,5] = self.fk_c
H[5,3] = H[3,5].conj()
H[4,6] = self.fk_c
H[6,4] = H[4,6].conj()
return H
def H11_12(self, k):
#H11_12 1st
H =np.zeros((7,7), dtype=complex)
H[0,2] = self.J1*np.exp(-1.j*k.dot(L2))
H[1,5] = self.J1*np.exp(-1.j*k.dot(L1))
H[2,0] = self.J1
H[3,3] = self.J1*np.exp(-1.j*k.dot(L2))
H[4,6] = self.J1*np.exp(-1.j*k.dot(L2))
H[6,0] = self.J1
H[6,4] = self.J1
#2nd
H[0,1] = self.fk * np.exp(-1.j*k.dot(L2))
H[0,3] = self.fk_c * np.exp(-1.j*k.dot(L2))
H[0,5] = self.fk_c * np.exp(-1.j*k.dot(L1))
H[1,0] = self.fk_c
H[1,2] = self.fk_c * np.exp(-1.j*k.dot(L2))
H[1,4] = self.fk_c * np.exp(-1.j*k.dot(L1))
H[1,6] = self.fk * np.exp(-1.j*k.dot(L1))
H[2,1] = self.fk_c
H[2,3] = self.fk * np.exp(-1.j*k.dot(L2))
H[2,5] = self.fk * np.exp(-1.j*k.dot(L1))
H[3,0] = self.fk
H[3,2] = self.fk * np.exp(-1.j*k.dot(L2))
H[3,4] = self.fk_c * np.exp(-1.j*k.dot(L2))
H[3,6] = self.fk * np.exp(-1.j*k.dot(L2))
H[4,1] = self.fk_c * np.exp(-1.j*k.dot(L2-L1))
H[4,3] = self.fk_c * np.exp(-1.j*k.dot(L2))
H[4,5] = self.fk * np.exp(-1.j*k.dot(L2))
H[5,0] = self.fk_c
H[5,2] = self.fk * np.exp(-1.j*k.dot(L2-L1))
H[5,4] = self.fk
H[5,6] = self.fk_c * np.exp(-1.j*k.dot(L2))
H[6,1] = self.fk
H[6,3] = self.fk_c
H[6,5] = self.fk
return H
def H11_21(self, k):
return np.conjugate(self.H11_12(k)).T
def H11_22(self, k):
H =np.zeros((7,7), dtype=complex)
H[0,1] = self.J1
H[1,0] = self.J1
H[1,2] = self.J1
H[2,1] = self.J1
H[1,6] = self.J1*np.exp(-1.j*k.dot(L1))
H[6,1] = self.J1*np.exp(1.j*k.dot(L1))
H[2,3] = self.J1
H[3,2] = self.J1
H[3,4] = self.J1
H[4,3] = self.J1
H[4,4] = -self.Jc
H[4,5] = self.J1
H[5,4] = self.J1
H[5,6] = self.J1
H[6,5] = self.J1
#2nd
H[0,2] = self.fk
H[2,0] = H[0,2].conj()
H[0,4] = self.fk_c
H[4,0] = H[0,4].conj()
H[0,6] = self.fk_c*np.exp(-1.j*k.dot(L1))
H[6,0] = H[0,6].conj()
H[1,3] = self.fk
H[3,1] = H[1,3].conj()
H[1,5] = self.fk_c*np.exp(-1.j*k.dot(L1))
H[5,1] = H[1,5].conj()
H[2,4] = self.fk
H[4,2] = H[2,4].conj()
H[2,6] = self.fk*np.exp(-1.j*k.dot(L1))
H[6,2] = H[2,6].conj()
H[3,5] = self.fk_c
H[5,3] = H[3,5].conj()
H[4,6] = self.fk_c
H[6,4] = H[4,6].conj()
return H
def H12_11(self, k):
H =np.zeros((7,7), dtype=complex)
H[2,2] = self.Jc
return H
def H12_22(self, k):
H =np.zeros((7,7), dtype=complex)
H[4,4] = self.Jc
return H
def H22_11(self, k):
#H11_11
H =np.zeros((7,7), dtype=complex)
H[0,1] = self.J1
H[1,0] = self.J1
H[0,5] = self.J1*np.exp(-1.j*k.dot(L2))
H[5,0] = H[0,5].conj()
H[1,2] = self.J1
H[2,1] = self.J1
H[2,2] = -self.Jc
H[2,3] = self.J1
H[3,2] = self.J1
H[3,4] = self.J1
H[4,3] = self.J1
H[4,5] = self.J1
H[5,4] = self.J1
H[5,6] = self.J1
H[6,5] = self.J1
#2nd
H[0,2] = self.fk
H[2,0] = H[0,2].conj()
H[0,4] = self.fk_c*np.exp(-1.j*k.dot(L2))
H[4,0] = H[0,4].conj()
H[0,6] = self.fk*np.exp(-1.j*k.dot(L2))
H[6,0] = H[0,6].conj()
H[1,3] = self.fk
H[3,1] = H[1,3].conj()
H[1,5] = self.fk*np.exp(-1.j*k.dot(L2))
H[5,1] = H[1,5].conj()
H[2,4] = self.fk_c
H[4,2] = H[2,4].conj()
H[2,6] = self.fk
H[6,2] = H[2,6].conj()
H[3,5] = self.fk_c
H[5,3] = H[3,5].conj()
H[4,6] = self.fk_c
H[6,4] = H[4,6].conj()
return H
def H22_12(self, k):
#H11_12
H =np.zeros((7,7), dtype=complex)
H[0,2] = self.J1*np.exp(-1.j*k.dot(L1))
H[1,5] = self.J1*np.exp(-1.j*k.dot(L2))
H[2,0] = self.J1
H[3,3] = self.J1*np.exp(-1.j*k.dot(L1))
H[4,6] = self.J1*np.exp(-1.j*k.dot(L1))
H[6,0] = self.J1
H[6,4] = self.J1
#2nd
H[0,1] = self.fk * np.exp(-1.j*k.dot(L1))
H[0,3] = self.fk_c * np.exp(-1.j*k.dot(L1))
H[0,5] = self.fk_c * np.exp(-1.j*k.dot(L2))
H[1,0] = self.fk_c
H[1,2] = self.fk_c * np.exp(-1.j*k.dot(L1))
H[1,4] = self.fk_c * np.exp(-1.j*k.dot(L2))
H[1,6] = self.fk * np.exp(-1.j*k.dot(L2))
H[2,1] = self.fk_c
H[2,3] = self.fk * np.exp(-1.j*k.dot(L1))
H[2,5] = self.fk * np.exp(-1.j*k.dot(L2))
H[3,0] = self.fk
H[3,2] = self.fk * np.exp(-1.j*k.dot(L1))
H[3,4] = self.fk_c * np.exp(-1.j*k.dot(L1))
H[3,6] = self.fk * np.exp(-1.j*k.dot(L1))
H[4,1] = self.fk_c * np.exp(-1.j*k.dot(L2-L1))
H[4,3] = self.fk_c * np.exp(-1.j*k.dot(L1))
H[4,5] = self.fk * np.exp(-1.j*k.dot(L1))
H[5,0] = self.fk_c
H[5,2] = self.fk * np.exp(-1.j*k.dot(L2-L1))
H[5,4] = self.fk
H[5,6] = self.fk_c * np.exp(-1.j*k.dot(L1))
H[6,1] = self.fk
H[6,3] = self.fk_c
H[6,5] = self.fk
return H
def H22_21(self, k):
return np.conjugate(self.H22_12(k)).T
def H22_22(self, k):
H =np.zeros((7,7), dtype=complex)
H[0,1] = self.J1
H[1,0] = self.J1
H[1,2] = self.J1
H[2,1] = self.J1
H[1,6] = self.J1*np.exp(-1.j*k.dot(L2))
H[6,1] = self.J1*np.exp(1.j*k.dot(L2))
H[2,3] = self.J1
H[3,2] = self.J1
H[3,4] = self.J1
H[4,3] = self.J1
H[4,4] = -self.Jc
H[4,5] = self.J1
H[5,4] = self.J1
H[5,6] = self.J1
H[6,5] = self.J1
#2nd
H[0,2] = self.fk
H[2,0] = H[0,2].conj()
H[0,4] = self.fk_c
H[4,0] = H[0,4].conj()
H[0,6] = self.fk_c*np.exp(-1.j*k.dot(L2))
H[6,0] = H[0,6].conj()
H[1,3] = self.fk
H[3,1] = H[1,3].conj()
H[1,5] = self.fk_c*np.exp(-1.j*k.dot(L2))
H[5,1] = H[1,5].conj()
H[2,4] = self.fk
H[4,2] = H[2,4].conj()
H[2,6] = self.fk*np.exp(-1.j*k.dot(L2))
H[6,2] = H[2,6].conj()
H[3,5] = self.fk_c
H[5,3] = H[3,5].conj()
H[4,6] = self.fk_c
H[6,4] = H[4,6].conj()
return H
def model(self, k):
kx, ky = k
H1_up = np.concatenate((self.H11_11(k), self.H11_12(k)), axis=1)
H1_dn = np.concatenate((self.H11_21(k), self.H11_22(k)), axis=1)
H1 = np.concatenate((H1_up, H1_dn), axis=0)
H2_up = np.concatenate((self.H22_11(k), self.H22_12(k)), axis=1)
H2_dn = np.concatenate((self.H22_21(k), self.H22_22(k)), axis=1)
H2 = np.concatenate((H2_up, H2_dn), axis=0)
H_jc_1 = np.concatenate((self.H12_11(k), np.zeros((7,7),dtype=complex)), axis=1)
H_jc_2 = np.concatenate((np.zeros((7,7),dtype=complex), self.H12_22(k)), axis=1)
H_jc1 = np.concatenate((H_jc_1, H_jc_2), axis=0)
H_jc2 = np.conjugate(H_jc1).T
H_up = np.concatenate((H1, H_jc1), axis=1)
H_dn = np.concatenate((H_jc2, H2), axis=1)
H = np.concatenate((H_up, H_dn), axis=0)
Htt = (self.A0 + self.tt * (kx + ky)) * np.eye(28, dtype=complex)
return np.array(H + Htt )
if __name__ == "__main__":
FM = twist_FM_1()
H = FM.model(np.array([1,1]))
print(H.shape)