Dear all,
thanks in advance for the support.
As I already had occasion to explain to Xavier, my problem concerns a
ring geometry where changing Hamiltonian values on non-existing sites
inside the ring (r<r1) actually changes the conductance behavior, while
it should not.
More precisely, I am building a ring, assigning to the ring sites a
certain value given by the/onsite/ function, which however in its
definition contains a conditional /if-/instruction involving sites
inside the ring.
I was expecting that the /if-/condition is then never satisfied and thus
no change is made, but the conductance curve changes if I change the
values of, say, the chemical potential (on-site energy) inside the ring,
where no sites exist.
However, If I do the /same/ changes /outside/ the ring (r>r2), no change
occurs in the conductance, as it should.
Of course one hypothesis is that I am in fact changing also Hamiltonian
elements of the ring, but I don't see why.
As suggested by Xavier, I will try to check that by using plotter.
I attach the piece of code.
I put a comment on the line where I write the conditional instruction
for mu.
If you try to run the code for different values of mu_inside, and/or
different physical sub-regions inside the ring, you should see different
conductance behavior.
I am using python 2.7.5 on a Mac OS X 10.6.8 and the same holds true for
a Mac OS X 10.8.5.
Thanks a lot in advance for any hint on how to understand this misbehavior.
Diego
==============================================================================
import kwant
import scipy, scipy.io
from numpy import *
from pylab import *
import sys
from numpy import mod
from math import pi,atan2
import matplotlib as mpl
from matplotlib import pyplot
import random; import pickle
params = {'backend': 'pdf',
'ytick.direction': 'out',
'text.usetex': True,
'font.size':16}
rcParams.update(params)
matplotlib.rcParams.update({'font.size': 20})
im=0+1j
import tinyarray
import scipy.sparse.linalg
class SimpleNamespace(object):
"""A simple container for parameters."""
def __init__(self, **kwargs):
self.__dict__.update(kwargs)
s_0 = identity(2)
s_z = array([[1, 0], [0, -1]])
s_x = array([[0, 1], [1, 0]])
s_y = array([[0, -1j], [1j, 0]])
#=================================================================================
def make_system(a=1, W=10, r1=10, r2=20):
lat = kwant.lattice.square(a)
sys = kwant.Builder()
def ring(pos):
(x, y) = pos
rsq = x ** 2 + y ** 2
return (r1 ** 2 < rsq < r2 ** 2)
def mu(site, p):
(x, y) = site.pos
if abs(x) < r1 and abs(y) < r1:
return p.mu_inside # this is the critical line: changing
mu values inside the ring should not change the ring conductance
else:
return p.mu_ring
def onsite(site, p):
return ( 4.0 * p.t - mu(site, p)) * s_0
def hopping(site0, site1, p):
return -p.t * s_0
#
===============================================================================
sys[lat.shape(ring, (0, r1 + 1))] = onsite
sys[lat.neighbors()] = hopping
#
===================================================================================
sym_lead = kwant.TranslationalSymmetry((-a, 0))
lead = kwant.Builder(sym_lead)
def lead_shape(pos):
(x, y) = pos
return (-W / 2 < y < W / 2)
lead[lat.shape(lead_shape, (0, 0))] = onsite
lead[lat.neighbors()] = hopping
sys.attach_lead(lead)
sys.attach_lead(lead.reversed())
return sys
def plot_conductance(sys, energies, p):
data = []
for energy in energies:
smatrix = kwant.smatrix(sys, energy, args=[p])
data.append(smatrix.transmission(1, 0))
axes([0.12, 0.12, 0.8, 0.8])
hold(True)
pyplot.plot(energies, data, 'bo-', ms=2.8,
linewidth=0.5,markeredgewidth=0.03)
pyplot.axis([0, 3.0, 0, 10.1])
pyplot.xlabel(r'$eV[t]$')
pyplot.ylabel(r'$G[e^2/h]$')
savefig('Ring_G(e).pdf')
def main():
sys = make_system()
kwant.plot(sys)
sys = sys.finalized()
params = SimpleNamespace(t=1.0, mu_ring=0.0, mu_inside=-1.62)
pyplot.figure()
plot_conductance(sys, energies=[0.01 * i for i in xrange(300)],
p=params)
if __name__ == '__main__':
main()
==================================================================================