Mailman 3 November 2016 - 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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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

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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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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

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Question regarding orbitals and scattering matrix
by Camilla Espedal Nov. 27, 2016

Nov. 27, 2016

Hi again, This question is sort of related to one of mye previous questions (https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg01029.html) but I am writing it as a new one. The questions relates to the sites in the lead unit cell and the scattering matrix. Say I have a system (simple 2D wire), where I have 3 sites in my unit cell (3 orbitals). I then make a system at an energy which is so low that I only have one propagating mode in the system. If I then run smatrix.lead_info[0] it returns a 2x3 matrix (which corresponds to left/right going and number of orbitals). If I then run smatrix.submatrix(0,0) I only get one element, which orbital does this element "belong" to, or how does it relate to these orbitals? Is the scattering matrix the same for all orbitals? Is the probability of scattering from say orbital 1 in one lead to orbital 2 in another the same as from orbital 1 to orbital 1? Hope my question makes sens. Best regards, Camilla

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Re: [Kwant] About some help to understand Physics
by Sudin Ganguly Nov. 24, 2016

Nov. 24, 2016

Dear Sir, If I calculate the Rashba term, (S \times d_ij)_z, for one case the Sigma_X terms comes out (in KWANT along (0,0) direction). That's why I have included this term in my system. There is no other reason. It feels that there may be something wrong in my calculation since you have said about the Sigma_z conservation. Can I show you my calculations. It'll not take much time, there are only 5-6 lines. Hope you don't mind. With Regards, Sudin > Dear Sudin, > > 1. I mean the conservation of sigma_z. > > 2. There is no motivation for it, that's just what you have done in your > code. > > Best, > Anton > > On Wed, Nov 23, 2016 at 10:44 PM, Sudin Ganguly <sudin(a)iitg.ernet.in> > wrote: >> Dear Sir, >> >> First of all, I would like to apologize in advance, if this mail bothers >> you. >> >> Today you send me reply about the smatrix for up and down spins in >> graphene. >> That was very much helpful to me. >> >> I would like to ask you about the conservation law in the leads, since >> it >> does not seem right to post this kind of question in KWANT forum. >> >> 1. is this Conservation law meant the current conservation? If this is >> so, >> how do I understand this. >> >> >> 2. Kane-Mele model said that in graphene there is NN Rashba interaction, >> and other is NNN intrinsic SO interaction. Then what is the motivation >> to >> avoid these kind of interactions in the leads. >> >> I'll be eagerly waiting for your reply. >> >> With Regards, >> Sudin >> >> -- >> ==================== >> Sudin Ganguly >> Research Scholar >> Dept. of Physics >> IIT Guwahati >> Assam,India-781039 >> =================== >

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Re: [Kwant] smatrix for up and down spin channels in graphene with KM Hamiltonian
by Sudin Ganguly Nov. 24, 2016

Nov. 24, 2016

Dear sir, I've implemented the same on square lattice, and the conductance is coming out as expected. But when I did the same on graphene, the expected result is not coming. With Regards, Sudin

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Re: [Kwant] Question about lead_info[].wave_functions[]
by Camilla Espedal Nov. 17, 2016

Nov. 17, 2016

Hi again, So my final question is then. What is the unit cell? Doesn't a square lattice only have one site per unit cell? Or is it the number of interface sites? Best, Camilla

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Re: [Kwant] Question about lead_info[].wave_functions[]
by Camilla Espedal Nov. 16, 2016

Nov. 16, 2016

Hi Joe, Thank you. This might be a silly question, but what is the meaning of orbitals here? Is it not only 1? The orbital elements seem to be conjugate of each other. Best, Camilla

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smatrix for up and down spin channels in graphene with KM Hamiltonian
by Sudin Ganguly Nov. 16, 2016

Nov. 16, 2016

Dear sir, I'm trying to get the transmission coefficients for up and down spin channels in graphene with Kane-Mele Hamiltonian (including Rashba term). So it needs to write the Hamiltonian for up and down spin separately. I started with this, sys=kwant.Builder() lat_u=kwant.lattice.honeycomb() lat_d=kwant.lattice.honeycomb() a,b= lat_u.sublattices c,d= lat_d.sublattices My confusion is that, can I declare these sublattices for up and down spins. With Regards, Sudin

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