Mailman 3 October 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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Symmetry and leads
by David Abergel Oct. 30, 2014

Oct. 30, 2014

Dear all, I am having a problem defining a system which matches what I want. I start by defining a rectangular graphene lattice of size 0<=x<L in the x direction and 0<=x<W in the y direction. (By "rectangular" I mean in the real space coordinates, not the crystallographic coordinates.) I want to attach a lead to the left-had end of this rectangle, going to minus infinity. Therefore, I define a lead with translational symmetry (-1,0) and the appropriate hopping. I attach the lead and plot the system. When I plot the system, I find that the lead has been attached along the (0,1) crystallographic direction (so, that is along the (1/2, sqrt(3)/3) real space vector). A triangle of extra sites have been added for x<0 (real space) so that the total shape of the scattering region is now not rectangular. If I attach another lead with lead.reversed(), a similar thing happens on the right of the sample so that my scattering region is now a parallelogram. As I understand it, this should not affect the physics in any way, since the lead is semi-infinite. But, if I want to draw pictures, plot functions over the scattering region, and gain physical understanding, it is a bit of a pain. So, my question is whether there is any way to make the lead attach along the (0,1) real space direction (which is the same as the (-1,2) crystallographic direction) and yet maintain the (-1,0) translational symmetry? If you require a sample program which reproduces this behavior then I can easily provide that, but I thought I should not extend an already long post unnecessarily. Thanks in advance. David

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Density of States and Fermi-Dirac
by Daniel Rodgers-Pryor Oct. 24, 2014

Oct. 24, 2014

Hi, Firstly, thanks for creating Kwant - it's so nice to use physics code written by people who understand software-engineering as well as physics :) I've got a few questions about units and density-of-states in Kwant, please respond if you know anything about any of them; don't feel the need to respond to them all at once. I'm trying to add self-consistent electrostatics to my Kwant system (using FiPy as a finite-element/volume Poisson-solver). Obviously, I need to calculate the electron-carrier-density of the system by integrating over the Fermi-Dirac occupation, then feed that (via real-space basis functions) to my Poisson solver. I'm not quite sure how to handle the density of states in the context of Kwant: I assume that just summing over the LDOS (integrating over all space) will give the density of states as a function of energy, D(E). Plotting it seems to produce reasonable bands, but I'm not quite sure about the units, or how it scales with system size. In the system I'm modelling (low-temperature p-donors in silicon), every lattice site adds an electron to the system (the temperatures are low enough that the silicon is frozen-out as a conductor and can just be treated as a background dielectric constant). I should be able to integrate over the density-of-states until the total equals the (known) number of electrons, but the density of states obtained by summing over the LDOS calculated by Kwant does not scale properly with the number of sites in the system; larger systems always need higher Fermi energies, which isn't physical at all. What am I missing here? Are the units of the LDOS Kwant calculates somehow normalised? How can I get a density-of-states which scales appropriately with the total number of electrons/sites in my system? The lead unit-cell of my system will need to be solved self-consistently too; how can I calculate the local density of states (and thus, via Fermi-Dirac, the electron-density) of a lead? Am I correct in assuming that the LDOS produced by Kwant is equivalent to summing over the state-density-weighted scattering-wavefunctions from the modes in all leads (and thus that integrating it over the occupied-energies will produce a sensible total electron-density)? Finally, and slightly unrelated, do my chosen energy-units need to be accounted-for anywhere in Kwant's Schroedinger-solutions? I'm writing my Hamiltonian terms in meV; will bands, LDOS etc. all naturally scale to make this choice transparent? Similarly, does effective electron-mass need to be accounted for at all? Thanks so much for your help, Daniel R-P

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About temprature and magnetic field control
by ANANT Oct. 4, 2014

Oct. 4, 2014

Dear all, Can we really use temperature variable in KWANT? If yes,then with what function.Also, How to apply magnetic field perpendicular to the sample like I am having the graphene sheet and I want to apply per mag. field on it.this is what I am trying! ################################################ def hopx(site1, site2, B=0): # The magnetic field is controlled by the parameter B y = site1.pos[1] return -t * exp(-1j * B * y) sys[lat.shape(circle, (0, 0))] = 4 * t # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = -t # It’s a closed system for a change, so no leads ##################################################

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