Mailman 3 January 2017 - 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))

3 3

Spin polarized transport calculation
by L.M J March 6, 2022

March 6, 2022

Dear Kwant users and developers I have two questions related to the spin calculation using kwant. 1. I'm wondering if we can do spin-polarized transport in kwant? For example, can we can get the separate Conductance Vs Energy diagram for spin up and spin down terms. I'm thinking one way of doing this is to set up the Rashba Hamiltonian as a whole. And then manually extract the spin up and spin down hamiltonian and do the transport calculation separately. But this will eliminate some extra terms that I don't know whether this is correct anymore. Any suggestions? 2. How can we set up the spin polarization for a particular site? For example, in some of the topological insulator, can we set up spin polarization on the edge as up and the other side of the edge as down, and then do the transport? Or this question is completely wrong? Thanks for advance. Sincerely, Liming

3 3

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

4 3

Using Kwant for finding tunneling probability from metal to vacuum
by Kristjan Eimre Feb. 14, 2017

Feb. 14, 2017

Hello Kwant experts, I have studied Kwant a bit, but before I delve deeper into it, I want to know if it can be applied to my problem. I have a 3d electron potential landscape for a metal-vacuum surface calculated with DFT. (More detailed info and pictures in [1]). Can I use Kwant to calculate the transmission probability of electrons incident on the surface? And if kwant is not suitable for this problem, perhaps you know of any other numerical software or method that would allow this calculation? [1] - http://physics.stackexchange.com/questions/295329/quantum-tunneling-probabi… Best regards, Kristjan

5 9

Re: [Kwant] How to attach the leads manually?
by Татьяна Григоренко Jan. 31, 2017

Jan. 31, 2017

TranslationalSymmetry does not work with my SimpleSite Family. Therefore, I attach the leads manually. I Use class kwant.builder.BuilderLead(builder, interface). I define a builder in the following way: #The tight-binding system of a left lead. left_lead = kwant.Builder() #Add sites lead left_lead[lat(x1, y1)] = 1.5 left_lead[lat(x2, y2)] = 1.5 etc #Add hoppings left_lead[lat(x2, y2), lat(x1, y1)] = 2j etc The same way I define the interface(wich called left_sequence) but without the hoppings. l_lead = kwant.builder.BuilderLead(left_lead, left_sequence). But it does not work. Where I'm wrong? As the lead I want to use the left and right boundary of my graphene atoms. С уважением, Татьяна Григоренко

1 0

Regarding smatrix and spin
by Camilla Espedal Jan. 24, 2017

Jan. 24, 2017

Hi again, This question is basically the same as this: https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00076.html I want to calculate some things using the scattering matrix. I started out with a very simple system, most basic two-terminal system. For some energy there is one propagating mode. I now add matrix structure to the mix (just multiply by s_0 everywhere) and there are now 2 propagating modes (which makes sense). Now, if I look at the reflection coefficients for lead 0 by using submatrix(0,0), it is now a 2x2 matrix after I introduced the matrices. How are the elements ordered? Is it [[r_upup, r_updown],[r_downup, r_downdown]] I know that I could make two lattices, but since I do not plan to use the other functions such as transmission. I just want the smatrix. Hope you can help me, and thanks in advance. Best regards, Camilla

4 9

Regarding tranlational invariance along 2 directions
by ANANT VIJAY Jan. 24, 2017

Jan. 24, 2017

Hello everyone, I am writing this to ask about how can I finalize the sytem with translational invariance along two directions. Code that I am using is the following as I want to make a slab system for band structure. sym = kwant.TranslationalSymmetry([1, 0, 0], [0, 1, 0]) Error: ValueError: Currently, only builders without or with a 1D translational symmetry can be finalized. Is there any solution to this? I also happen to get one code from notes on internet by edx course where thwe following code has been used using wraparound function. I did not get much out of it. Also, I checked I don't have this function in my kwant module. how can I get this functions module? Please anyone can explian what this function is doing in the code: def make_scatter_sys(): from functions import wraparound syst = wraparound(bhz(Z=1, system_type='slab')) syst.attach_lead(make_lead()) syst.attach_lead(wraparound(bhz(), keep=0)) syst = syst.finalized() syst.leads[0] = TRIInfiniteSystem(syst.leads[0], trs) return syst ANANT VIJAY VARMA Research Scholar IISER-KOLKATA WEST BENGAL.

2 1

Installation instructions for Kwant on WSL
by Anton Akhmerov Jan. 23, 2017

Jan. 23, 2017

Hi everyone, Andrey Antipov kindly shared his installation instructions for Kwant using the Windows subsystem for Linux. If you are interested, please check it out over here: https://gist.github.com/aeantipov/3839d09529cb5dd2cedc00b76ccd2eb8 Best, Anton

4 4

Re: [Kwant] Units of the wavefunction and velocity
by Harshad Sahasrabudhe Jan. 23, 2017

Jan. 23, 2017

Great, thanks a lot! On Mon, Jan 23, 2017 at 10:15 AM, Anton Akhmerov < anton.akhmerov+kd(a)gmail.com> wrote: > > Thank you. Then to calculate the velocity, should I just divide the > > probability current by the integral of |𝜓|2 over the unit cell? > > You could do that, but this is already done in Kwant, and you can read > the velocities off from the modes object [1]. > > Best, > Anton > > [1]: https://kwant-project.org/doc/1/reference/generated/kwant. > physics.PropagatingModes#kwant.physics.PropagatingModes >

2 3

Units of the wavefunction and velocity
by Harshad Sahasrabudhe Jan. 23, 2017

Jan. 23, 2017

Hi, I was wondering what units would the wavefunction obtained from Kwant have? I was thinking they would have the units 1/sqrt(nm.eV) (since my energies are in eV and lengths are in nm) as the modes are normalized according to [image: Inline image 1] How would I calculate the velocity of the mode, if the modes are normalized to carry unit current? Thanks, Harshad

2 4