graphene.py

#!/usr/bin/env python

# Toy graphene model

# Copyright under GNU General Public License 2010, 2012, 2016
# by Sinisa Coh and David Vanderbilt (see gpl-pythtb.txt)

from __future__ import print_function
from pythtb import * # import TB model class
import numpy as np
import matplotlib.pyplot as plt

# define lattice vectors
lat=[[1.0,0.0],[0.5,np.sqrt(3.0)/2.0]]
# define coordinates of orbitals
orb=[[1./3.,1./3.],[2./3.,2./3.]]

# make two dimensional tight-binding graphene model
my_model=tb_model(2,2,lat,orb)

# set model parameters
delta=0.0
t=-1.0

# set on-site energies
my_model.set_onsite([-delta,delta])
# set hoppings (one for each connected pair of orbitals)
# (amplitude, i, j, [lattice vector to cell containing j])
my_model.set_hop(t, 0, 1, [ 0, 0])
my_model.set_hop(t, 1, 0, [ 1, 0])
my_model.set_hop(t, 1, 0, [ 0, 1])

# print tight-binding model
my_model.display()
    
# generate list of k-points following a segmented path in the BZ
# list of nodes (high-symmetry points) that will be connected
path=[[0.,0.],[2./3.,1./3.],[.5,.5],[0.,0.]]
# labels of the nodes
label=(r'$\Gamma $',r'$K$', r'$M$', r'$\Gamma $')
# total number of interpolated k-points along the path
nk=121

# call function k_path to construct the actual path
(k_vec,k_dist,k_node)=my_model.k_path(path,nk)
# inputs:
#   path, nk: see above
#   my_model: the pythtb model
# outputs:
#   k_vec: list of interpolated k-points
#   k_dist: horizontal axis position of each k-point in the list
#   k_node: horizontal axis position of each original node

print('---------------------------------------')
print('starting calculation')
print('---------------------------------------')
print('Calculating bands...')

# obtain eigenvalues to be plotted
evals=my_model.solve_all(k_vec)

# figure for bandstructure

fig, ax = plt.subplots()
# specify horizontal axis details
# set range of horizontal axis
ax.set_xlim(k_node[0],k_node[-1])
# put tickmarks and labels at node positions
ax.set_xticks(k_node)
ax.set_xticklabels(label)
# add vertical lines at node positions
for n in range(len(k_node)):
  ax.axvline(x=k_node[n],linewidth=0.5, color='k')
# put title
ax.set_title("Graphene band structure")
ax.set_xlabel("Path in k-space")
ax.set_ylabel("Band energy")

# plot first and second band
ax.plot(k_dist,evals[0])
ax.plot(k_dist,evals[1])

# make an PDF figure of a plot
fig.tight_layout()
fig.savefig("graphene.pdf")

print('Done.\n')