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Haldane_model.py
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# -*- coding: utf-8 -*-
"""
Spyder Editor
Python script to calculate the Kane-mele band
Author: Jinyang Ni
"""
import numpy as np
import matplotlib.pyplot as plt
from math import pi
from band_ini import config as cf
#spin exchange parameters
#define the Hamiltonian
class Honeycomb():
def __init__(self, t1=1, t3 = 1, D1=0, ):
self.H =np.zeros((2,2), dtype=complex)
self.t1 = t1
self.t3 = t3
self.D1 = D1
self.J2 = 0
self.A = 0
self.A0 = 0.0
self.tt = -0.0 # titling term
def model(self, k):
kx, ky = k
gk = self.t1 * np.exp(1.j*k.dot(cf.a1)) + self.t1*np.exp(1.j*k.dot(cf.a2)) + self.t3*np.exp(1.j*k.dot(cf.a3))
self.H[0,1] = gk
self.H[1,0] = gk.conj()
#add NNN conj hopping term
dk = 2*np.sin(k.dot(cf.d1)) + np.sin(k.dot(cf.d2)) + np.sin(k.dot(cf.d3))
Hd = self.D1*dk * cf.sz
jk = self.J2*(2*(np.cos(k.dot(cf.d1)) + np.cos(k.dot(cf.d2)) + np.cos(k.dot(cf.d3))) - 6)
H2 = jk * cf.sz + self.A * cf.sz + self.A0 * cf.s0 + self.tt*(kx + ky) * cf.s0
return np.array(self.H + Hd + H2)
class Zigzag():
def __init__(self):
self.H =np.zeros((4,4), dtype=complex)
self.t1 = -2
self.D1 = 0.1
self.J2 = 0.0
self.M1 = -0.21
self.M2 = -0.21
self.M3 = 0.2
self.M4 = 0.2
self.tt = -0.0 # titling term
def model(self, k):
kx, ky = k
g1k = self.t1 * (np.exp(1.j*k.dot(cf.az2)) + np.exp(1.j*k.dot(cf.az3)))
g2k = self.t1*np.exp(1.j*k.dot(cf.az1))
f1k = self.D1*np.sin(k.dot(cf.dz2))
f2k = self.D1*(np.sin(k.dot(cf.dz1)) + np.sin(k.dot(cf.dz3)))
self.H[0,1] = g1k
self.H[1,0] = g1k.conj()
self.H[0,2] = g2k
self.H[2,0] = g2k.conj()
self.H[1,3] = g2k.conj()
self.H[3,1] = g2k
self.H[2,3] = g1k.conj()
self.H[3,2] = g1k
self.H[0,0], self.H[1,1], self.H[2,2], self.H[3,3] = self.M1 + f1k, self.M2-f1k, self.M3-f1k, self.M4+f1k
self.H[0,3], self.H[1,2], self.H[2,1], self.H[3,0] = f2k, -f2k, -f2k, f2k
#adding titlting term
Htt = self.tt*(kx) * np.eye(4, dtype=complex)
return np.array(self.H + Htt)
class stripe():
def __init__(self):
self.H =np.zeros((4,4), dtype=complex)
self.t1 = -1
self.D1 = 0.1
self.J2 = 0.0
self.M1 = 0.2
self.M2 = -0.2
self.M3 = 0.2
self.M4 = -0.2
self.tt = -0.0 # titling term
def model(self, k):
kx, ky = k
g1k = self.t1 * (np.exp(1.j*k.dot(cf.az2)) + np.exp(1.j*k.dot(cf.az3)))
g2k = self.t1*np.exp(1.j*k.dot(cf.az1))
f1k = self.D1*np.sin(k.dot(cf.dz2))
f2k = self.D1*(np.sin(k.dot(cf.dz1)) + np.sin(k.dot(cf.dz3)))
self.H[0,1] = g1k
self.H[1,0] = g1k.conj()
self.H[0,2] = g2k
self.H[2,0] = g2k.conj()
self.H[1,3] = g2k.conj()
self.H[3,1] = g2k
self.H[2,3] = g1k.conj()
self.H[3,2] = g1k
self.H[0,0], self.H[1,1], self.H[2,2], self.H[3,3] = self.M1 + f1k, self.M2-f1k, self.M3-f1k, self.M4+f1k
self.H[0,3], self.H[1,2], self.H[2,1], self.H[3,0] = f2k, -f2k, -f2k, f2k
#adding titlting term
Htt = self.tt*(kx) * np.eye(4, dtype=complex)
return np.array(self.H + Htt)