Hello, I am trying to simulate the quantum hall effect in a hall bar made of a honeycomb (graphene) lattice. I modified the code submitted by C. Groth as a response to a 2015 thread (link below). As soon as I add the vertical leads, I cant seem to get the expected phenomenon for both longitudinal and hall resistances. Here is my code, if anyone spots an error or a solution, do let me know!

Sid Sule --------------------------------------------

from cmath import exp import numpy from matplotlib import pyplot

import kwant from kwant.digest import gauss

def hopping(sitei, sitej, phi, salt): xi, yi = sitei.pos xj, yj = sitej.pos return -exp(-0.5j * phi * (xi - xj) * (yi + yj))

def onsite(site, phi, salt): return 0.05 * gauss(repr(site), salt)

def make_system(L=20, W=30):

def central_region(pos): x, y = pos return abs(x) < (W/2) and abs(y) < (L/2)

lat = kwant.lattice.honeycomb() sys = kwant.Builder()

sys[lat.shape(central_region, (0, 0))] = onsite sys[lat.neighbors()] = hopping

vertices = numpy.array([[-15, -6, 5, 10], [-15, -6, -10, -5], [6, 15, 5, 10], [6, 15, -10, -5], [-2, 2, 5, 10], [-2, 2, -10, -5]])

for v in vertices:

def in_hole(site):

x, y = site.pos return (v[0] <= x <= v[1]) and (v[2] <= y <= v[3])

for site in filter(in_hole, list(sys.sites())):

del sys[site]

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

lead[lat.shape(lambda s: abs(s[1]) < (L/4), (0, 0))] = 0 lead[lat.neighbors()] = hopping

sys.attach_lead(lead) sys.attach_lead(lead.reversed())

edges = numpy.array([[-6, -2, -4], [2, 6, 4]])

for e in edges:

sym = kwant.TranslationalSymmetry([0, numpy.sqrt(3)]) lead = kwant.Builder(sym)

def lead_region(pos):

x, y = pos return (e[0] < x < e[1])

lead[lat.shape(lead_region, (e[2], 0))] = 0 lead[lat.neighbors()] = hopping

sys.attach_lead(lead) sys.attach_lead(lead.reversed())

for x in lead.sites(): x.family.norbs = None

return sys.finalized()

sys = make_system() kwant.plot(sys, site_lw=0.1, lead_site_lw=0, colorbar=False, show=False)

energy = 0.35 reciprocal_phis = numpy.linspace(4, 50, 20)

current = numpy.array([-1, 1, 0, 0, 0, 0])

r_long = [] r_hall = [] for phi in 1 / reciprocal_phis:

params = {"phi": phi, "salt": ""}

smatrix = kwant.smatrix(sys, energy, params=params) cond_mat = smatrix.conductance_matrix()

# SOLVES FOR V IN I = G*V voltage = numpy.linalg.solve(cond_mat, current)

# DIVIDE BY 2 FOR V = I*R, I = 2 r_long.append(abs(voltage[2]-voltage[4]) / 2) r_hall.append((voltage[2] - voltage[3]) / 2)

fig, ax = pyplot.subplots(1, 1) ax.plot(reciprocal_phis, r_long) ax.plot(reciprocal_phis, r_hall)

fig.show()

--------------------- Link of original thread : https://mail.python.org/archives/list/kwant-discuss@python.org/thread/D3MTMB...