Dear all, thanks for all the answers. It is indeed due to the lead, I checked that now and it works if I separately define onsite for the lead without space-dependent conditions. That solves my problem, thanks a lot. Diego On 25/3/14 10:15 AM, Xavier Waintal wrote:
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 <mailto:xavier.waintal@cea.fr> http://inac.cea.fr/Pisp/xavier.waintal __________________________________________
Le 25 mars 2014 à 02:38, diego <diego.rainis@unibas.ch <mailto: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