Dear Diego,

I tried yours script and I think that the issue is the one spotted by Joe:

as leads are translationally invariant, you should also use functions to set their

Hamiltonian matrix elements that are translationally invariant as Kwant does not guarantee 

the results otherwise (indeed internally the lead is translated to the fundamental domain but you 

don't really need to know that).

The following script, adapted from yours, gives results which are independent from

p.mu_inside if you use onsite_lead or dependent if you use onsite on the line where one sets the 

lead matrix elements

Best regards,

Xavier

PS: the magic line to get the Hall resistance looks something like

   R= numpy.linalg.solve(G[:-1,:-1], [1, 0, -1])

where G is the transmission matrix in the Buttiker sense I = (e^2/h) G V

PPS: Michael was faster than me, but I post this anyway as you can run the script below directly

PPPS Joe, you're on vacation, remember?

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

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) < r1/2 and abs(y) < r1/2:

            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_lead(site, p):

        return ( 4.0 * p.t - p.mu_ring) * s_0

 

    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  # onsite_lead    CHANGE THIS TO GET DIFFERENT BEHAVIOR

    lead[lat.neighbors()]               = hopping

    sys.attach_lead(lead)

    sys.attach_lead(lead.reversed())

    return sys

def plot_conductance(sys, p):

    smatrix = kwant.smatrix(sys,3., args=[p])

    print "CONDUCTANCE: ",smatrix.transmission(1, 0)

    

def main():

    sys = make_system()

    kwant.plot(sys)

    sys = sys.finalized()

    params = SimpleNamespace(t=1.0, mu_ring=0.0, mu_inside=-1.02)

    plot_conductance(sys, p=params)

if __name__ == '__main__':

    main()

__________________________________________
Xavier Waintal
SPSMS-INAC-CEA,17 rue des Martyrs, 38054 Grenoble CEDEX 9, FRANCE
Tel: 33 (0)4 38 78 03 27 
email: xavier.waintal@cea.fr

http://inac.cea.fr/Pisp/xavier.waintal
__________________________________________

Le 25 mars 2014 à 02:38, diego <diego.rainis@unibas.ch> a écrit :

Hi,

thanks again for your time and your input.

I tried what you said, by setting by hand the onsite elements of the lead, but it's not solving the problem. The result is identical to the one with the previous onsite function.

Diego

On 25/3/14 2:04 AM, Joseph Weston wrote:

Hi again,

I've just had a thought as to what it could be, but I can't test it myself right now as I don't have access to a proper computer.

I think this may be due to the way that kwant handles leads.

When you create a Builder with a symmetry and add sites to it then kwant first translates the sites into the fundamental domain
of the symmetry and adds those to the Builder. For translational symmetries the fundamental domain is the one which contains

the point (0, 0). This means that when you construct your leads with::

    lead[lat.shape(lead_shape, (0, 0))] = onsite

then some of the onsites will actually evaluate to ``mu_inside`` as the lead sites satisfy the condition within ``onsite``.

You can test this hypothesis by setting the "sub-region" to something which does not include the lead's fundamental domain

(in your case a single line of sites in the y-direction between -W/2 and W/2 passing through the origin), or by setting the lead

onsites "manually" for testing.

Joe