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
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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()
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Link of original thread :
https://mail.python.org/archives/list/[email protected]/thread/D3MTMBACYBNXLQBOZTL46MTPP53F6FM3/#7E63YALHFD7J53ETVE4TNEKFOH5TNJLD
