Hi all.

I would like to know how to compute Hall conductance in a honeycomb lattice using Kwant. In my attempt, I started with the construction of the honeycomb lattice:

import kwant

import matplotlib.pyplot as plt

import numpy

from cmath import exp

from kwant.digest import gauss

lat = kwant.lattice.honeycomb()

sys = kwant.Builder()

def rectangle(pos):

x, y = pos

return 0 < x < 40 and 0 < y < 20

sys[lat.shape(rectangle, (1, 1))] = 0

sys[lat.neighbors()] = -1

sym = kwant.TranslationalSymmetry((-1, 0))

sym.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)])

sym.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)])

lead = kwant.Builder(sym)

def lead_shape(pos):

x, y = pos

return 0 < y < 20

lead[lat.shape(lead_shape, (-1,1))] = 4

lead[lat.neighbors()] = -1

sys.attach_lead(lead)

sys.attach_lead(lead.reversed())

My questions are:

How to attach another pair of leads at 13 < x < 15 and 23 < x < 25 with y = 10 and y =0? I tried

# For the 2nd Lead
sym2 = kwant.TranslationalSymmetry((-1, 0))

sym2.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)])
sym2.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)])

lead2 = kwant.Builder(sym)

def lead2_shape(pos2):
x, y = pos2
return 13 < x < 15, 10 < y < 10

lead[lat.shape(lead2_shape, (1,1))] = 4
lead[lat.neighbors()] = -1

sys.attach_lead(lead2)
sys.attach_lead(lead2.reversed())

but nothing works.

Also How to calculate hall conductance from these leads (assuming hopping is by Peierls substitution where t is replaced by an exponential)?

I am very new to the kwant program, as this is for an undergraduate research.

Regards,

James