Mailman 3 June 2014 - Kwant-discuss

How the spin is positioned in the Smatrix?
by Qingtian Zhang March 6, 2022

March 6, 2022

Dear all, I am trying square lattice with spin-orbit coupling and Zeeman splititng just like the example of Tutorial 2.3.1. Now I want to get the spin-dependent conductance：Guu,Gud,Gdu,and Gdd, where "u" indicates up spin, d indicates down spin. We can have the scattering matrix through Smatrix=kwant.smatrix(sys, energy), but how the spin is positioned in the scattering matrix? I have checked some simple cases, it seems the Smatrix is organized like this: | r t | S= | t' r' | but how the spin is included? Thanks in advance. Qingtiian Zhang The code is: import kwant from matplotlib import pyplot from numpy import matrix import tinyarray sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) sys=kwant.Builder() lat=kwant.lattice.square() a=1 t=1.0 alpha=0.5 e_z=0.08 W=2 L=2 sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) kwant.plot(sys) sys=sys.finalized() print "Hamiltonian=" print sys.hamiltonian_submatrix() Smatrix=kwant.smatrix(sys, energy=3.) print "The scattering matrix=" print matrix.round((Smatrix.data),2) print "T=",(Smatrix.transmission(1, 0))

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How to caculate hall resistance
by ZHANG Bing Sept. 12, 2021

Sept. 12, 2021

Dear Sir, I am a PhD student of Hong Kong University of Science and Technology. I want to use KWANT to caculate Hall resistance of a Hall bar structure.We can get the conductance between 6 electrodes, but how to get hall resistance? Can you give me some help? Thank you very much. Best Regards, Zhang Bing

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Incoherent transport
by Ted Pudlik July 1, 2014

July 1, 2014

Hello, Is it possible to use kwant to simulate incoherent transport processes (photon and phonon scattering) and compute quantities such as the optical conductivity? Has anyone ever done it? Best wishes, Ted Pudlik Boston University

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Re: [Kwant] actual grid position
by Jerzy Wrobel June 30, 2014

June 30, 2014

Joe, Thank you very much, that was exactly what I needed. Interestingly enough, when kwant.plotter.map(sys, ldos_array) is called again, AFTER dictionary creation, the resulting picture is changed to a random patchwork of colourful rectangles. Regards, Jerzy > On 30/06/14 08:55, Jerzy Wrobel wrote: >> Dear All, >> How to retrieve the actual grid position from a given site index? >> For example, how to get local_dos at (i,j) space position >> from 1d Numpy array, on a simple rectangular grid? >> I assume that it has something to do with pos method, but an >> simple example will be appreciated. >> Thanks in advance, >> Jerzy >> > > > Hi, > > The ordering of the elements of the output from `local_dos` (as well > as `wave_function`) is the same as the ordering of the sites in your > finalized system. You can say > > ldos_dict = {tuple(site.tag): ldos > for site, ldos in zip(fsys.sites, ldos_array)} > > where `fsys` is your finalized system and `ldos` is the numpy array > returned by `local_dos`. You can then get the value for site `(i,j)` > by saying > > ldos_dict[i, j] > > Note that this will only work in the case where you have 1 orbital per > site (i.e. scalar values for your onsite matrix elements). > > Hope that helps, > > Joe > >

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actual grid position
by Jerzy Wrobel June 30, 2014

June 30, 2014

Dear All, How to retrieve the actual grid position from a given site index? For example, how to get local_dos at (i,j) space position from 1d Numpy array, on a simple rectangular grid? I assume that it has something to do with pos method, but an simple example will be appreciated. Thanks in advance, Jerzy

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gauge invariance
by ZHANG Bing June 18, 2014

June 18, 2014

Dear Anton Akhmerov, I want to add magnetic field to a system with 6 electrodes. What gauge should I use? I tried two kinds of gauge. (1) A=(-B*y,0,0); (2) A=(0,B*x,0). But I found the conductance was different for different gauge, which was not reasonable. Can you help to solve this problem? Best Regards, Zhang Bing

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Hydrogenated graphene
by Cabosart Damien June 2, 2014

June 2, 2014

Dear all, Here is my question : Can we add an adatom to our graphene lattice using the kwant package? (For example, to get hydrogenated graphene with different hydrogen coverage) Thank you in advance for your help. Best regards, D. Cabosart

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