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Floquet_2D.py
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Floquet_2D.py
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# file Floquet_2D package
# contains functions needed for floquet lattice calculation.
# Author: Amin Ahmadi
# Date: 30 Jan, 2018
import numpy as np
############################################################
def make_sq(mlat, dAB, J):
"""Constructs the Hamiltonian and the connection
matrix of a bipartite square lattice.
0--o 0--o
| | | |
o--0 o--0
| | | |
0--o 0--o
One period of the driven field consists of 5 time
interval which are defined through hoping amplitude Ji
\in [1,2,..,5], where in the last interval all hopping
amplitude are off.
input:
------
mlat: integer, width of slab, number of site in
one super unitcell would br 2xm
J: is a tuple of float. Provide the hopping amplitude
for different time intrval
returns:
--------
h: 2mlatx2mlat complex matrix, Hamiltonian of the slab
tau: 2mlatx2mlat complex matrix, the connection matrix
between two neighbor super unit cell
"""
if (len(J)!=4):
print("Number of paramaters are exceeded 5!")
NN = 2*mlat
tau = np.zeros((NN,NN), dtype=complex)
h = np.zeros((NN,NN), dtype=complex)
for i in range(mlat-1):
if (i%2==0):
h[i,i] = dAB/2. # on-site energy
h[mlat+i,mlat+i] = -dAB/2. # on-site energy
h[i, mlat+i] = J[0]
h[i, i+1] = J[1]
h[mlat+i, mlat+i+1] = J[3]
#
tau[mlat+i, i] = J[2]
elif (i%2==1):
h[i,i] = -dAB/2. # on-site energy
h[mlat+i,mlat+i] = dAB/2. # on-site energy
h[i, mlat+i] = J[2]
h[i, i+1] = J[3]
h[mlat+i, mlat+i+1] = J[1]
#
tau[mlat+i, i] = J[0]
# End of loop over lattice sites
# The upper edge site
if (mlat-1 % 2==0):
h[mlat-1, mlat-1] = dAB/2. # on-site energy
h[NN-1,NN-1] = -dAB/2. # on-site energy
h[mlat-1, NN-1] = J[0]
#
tau[NN-1, mlat-1] = J[2]
elif (mlat-1 % 2==1):
h[mlat-1, mlat-1] = -dAB/2. # on-site energy
h[NN-1,NN-1] = dAB/2. # on-site energy
h[mlat-1, NN-1] = J[2]
#
tau[NN-1, mlat-1] = J[0]
h = h + h.conj().T # make it hermitian
return h, tau
############################################################
def make_Gr(mlat, J):
""" Constructs the Hamiltonian and the connection
matrix of an armchair graphene strip.
0--o 0--o
| | | |
o 0--o 0
| | | |
0--o 0--o
| | | |
o 0--o 0
| | | |
0--o 0--o
One period of the driven fieldconsists of 3 time
interval which are defined through hoping amplitude Ji
\in [1,2,3].
input:
------
mlat: integer, width of slab, number of site in
one super unitcell would br 2xm
returns:
--------
h: 2mlatx2mlat complex matrix, Hamiltonian of the slab
tau: 2mlatx2mlat complex matrix, the connection matrix
between two neighbor super unit cell
"""
if (len(J)!=3):
print("Number of paramaters are not right, must be 5!")
NN = 2*mlat # # of sites in one super unitcell
tau = -np.zeros((NN, NN),dtype=complex)
h = np.zeros((NN,NN), dtype=complex)
# translational cell's Hamiltonian
for i in range(mlat-1):
if (i%2==0):
h[i,i+1] = J[0]
h[mlat+i,mlat+i+1] = J[1]
h[i,mlat+i] = J[2] # horizoltal connection
elif (i%2==1):
h[i,i+1] = J[1]
h[mlat+i,mlat+i+1] = J[0]
# longitudinal connection of the last sites
if (mlat-1)%2 == 0:
h[mlat-1,2*mlat-1] = J[2]
h = h + h.conj().T # make it hermitian
# Hopping matrix
for i in range(1,mlat,2):
tau[i+mlat,i] = J[2]
return h, tau