Re: [Kwant] 3D Current Density

25 Mar 2020


      Thank you for the clarification.

Best Regards
Naveen Yadav
Research Scholar
Department of Physics & Astrophysics
University of Delhi
New Delhi-110007

On Wed, Mar 25, 2020, 18:50 Ousmane LY  wrote:
...
Dear Naveen,
if you want to use a 2d system to represent local properties of a 3d
system, the former shouldn’t be considered as a physical system. Therefore,
its onsite and hopping values are not relevant and shouldn’t alter your
calculations in any sens. Even attaching leads for the 2d system may not be
necessary.
However, you have to be sure that the 2d system represents well the 2d
plane of the underlying 3d geometry. This would concern mainly the number
of sites and links.
You may have a look to the illustration below.
Happy kwanting,
Ousmane,
############################################################
import kwant
def make_3d(L=5,W=5,H=5):
        # make a 3d system
        sys=kwant.Builder()
        lat=kwant.lattice.cubic(norbs=1)
        sys[(lat(x,y,z) for x in range(L) for y in range(W) for z in
range(H))]=0
        sys[lat.neighbors()]=-1
lead=kwant.Builder(kwant.TranslationalSymmetry((-1,0,0)))
        lead[(lat(0,y,z) for y in range(W) for z in range(H))] = -1
        lead[lat.neighbors()]=-1
        sys.attach_lead(lead)
return sys.finalized()
def make_2d(W=5,H=5):
        # make an auxiliary 2d system
        sys=kwant.Builder()
        lat=kwant.lattice.square()
        sys[(lat(y,z) for y in range(W) for z in range(H) )]= " "
        sys[lat.neighbors()]= " "
        return sys.finalized()
def main():
        # calculate the current at a given (y,z) plane
        given_x=0 # e.g
        def where(site1,site2):
                return site1.pos[0]==given_x and site2.pos[0]==given_x
psi=kwant.wave_function(make_3d(),energy=0)(0)[0] # lowest mode of
lead 0
        current=kwant.operator.Current(make_3d(), where=where)(psi)
# plot the current using the auxiliary 2d system
        kwant.plotter.current(make_2d(), current)
if __name__=='__main__':
    main()
##################################################################