Mailman 3 June 2015 - 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

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

New instructions for Windows installation
by Michael Wimmer Jan. 15, 2016

Jan. 15, 2016

Dear kwant users, we have posted new instructions for installing kwant on Windows on the kwant website: http://www.kwant-project.org/install The old instructions do not work any more, as the format of the python packages on Christoph Gohlke's webpage have changed. Best regards, the kwant team

3 3

Package for ubuntu vivid
by David Abergel Sept. 17, 2015

Sept. 17, 2015

Hi all, firstly, thanks so much for your work in developing and maintaining kwant. Hugely appreciated. Is there any chance you could package it for {,k,x}ubuntu 15.04? I tried installing kwant in that linux today, using the 14.10 package, and I am getting a bunch of errors from Tkinter and matplotlib when I use kwant's inbuilt plotter. Many thanks for your help David

2 3

Fresh install of kwant on OS X failed
by Bas Nijholt July 24, 2015

July 24, 2015

I’ve completely reinstalled my OS and am now encountering issues that I’ve heard other talk about, I’ve followed the instructions on the website word by word, except that I forked Michael’s repo and changed to kwant version 1.0.3. This has worked before for me. This is the error message: brew install kwant ==> Installing kwant from basnijholt/homebrew-kwant ==> Using Homebrew-provided fortran compiler. This may be changed by setting the FC environment variable. ==> Building with an alternative Fortran compiler This is unsupported. Warning: No Fortran optimization information was provided. You may want to consider setting FCFLAGS and FFLAGS or pass the `--default-fortran-flags` option to `brew install` if your compiler is compatible with GCC. If you like the default optimization level of your compiler, ignore this warning. ==> Downloading pypi.python.org/packages/source/k/kwant/kwant-1.0.3.tar.gz Already downloaded: /Library/Caches/Homebrew/kwant-1.0.3.tar.gz ==> Patching patching file build.conf ==> python setup.py install --prefix=/usr/local/Cellar/kwant/1.0.3 Build configuration was: User-configured LAPACK and BLAS User-configured MUMPS ********************************************************************** error: command 'clang' failed with exit status 1 READ THIS: https://git.io/brew-troubleshooting If reporting this issue please do so at (not Homebrew/homebrew): https://github.com/basnijholt/homebrew-kwant/issues Best Bas

5 6

Re: [Kwant] suggestion
by Sergey July 12, 2015

July 12, 2015

Dear Christoph, I use the following construction to connect the incommensurate lattices: lat_e (graphene) and lat_e1 (square) for x in list(lat_e1.shape(rectangle1, (0, 0))()): for neighbour in lat_e.sublattices[0].n_closest(x.pos): sys[(x, lat_e.sublattices[0](*neighbour))] = t01 for neighbour in lat_e.sublattices[1].n_closest(x.pos): sys[(x, lat_e.sublattices[1](*neighbour))] = t01 I hope it's clear why I want to improve n_closest Probably I can do that myself. The above construction may indeed be in the core of readymade function to connect the two lattices. Best wishes, Sergey

2 4

Plotting current density in Kwant
by Christoph Groth June 29, 2015

June 29, 2015

Dear all, I would like to discuss methods for plotting current densities in Kwant. Anyone is welcome to participate in this discussion. Please make sure that you always CC the mailing list in your replies. Wouldn’t it be nice if there was a nice standard way to plot current densities (and other vector fields) in Kwant? Now it is easy to calculate the current on each hopping of Kwant’s system graph (let’s assume that there is one orbital per site for simplicity), but how to display this information in a useful way that works for general graphs? Daniyar once implemented current density plotting that first smooths the vector field and then plots this using matplotlib’s streamplot. The result looks really nice (first attached image), but this method has at least one arbitrary parameter: the length scale of the smoothing. Adrien tried out an alternative “more direct” method inspired by [1]: the idea is to calculate the current on each hopping and interpret it as the flow of some (classical, i.e. not quantum) “liquid” between sites. In the beginning, the liquid of most sites is transparent, except for a few sites where it is colored by an “ink”. The second attached image shows a “long exposure” snapshot of this method for the QHE system of the Kwant paper. The ink intensity was set to 0 (white) for most sites and to 1 (black) for a few sites. Then, the intensity was let to evolve as described in the previous paragraph for some time. The image does not show the final state, but rather a time average over the evolution for some time. As you can see, the new method does not produce very nice images. In particular, streamlines do not behave isotropically: streamlines parallel to hoppings do not spread much, while diagonal ones spread dramatically. This is not surprising of course, but I think that the image is still interesting. What do you think would be a useful way to plot currents in Kwant? Daniyar’s method produces clearer pictures, but does interpolating the current densities on hoppings into a vector field actually make physical sense (on a general graph)? Is the anisotropy of the second method just an artifact (of disregarding coherence?), or is it actually a feature in some sense? I can imagine an interpolation scheme (Adrien implemented a proof-of-concept version already) that preserves the total current that pierces any given surface as an invariant. Given a graph with per-hopping currents, that interpolation method returns the currents that flow through the sides/faces of regularly spaced squares/cubes. This is not yet a vector field (because x- and y- components are spatially separated), but can be easily interpolated into one. I’m curious to hear what people think about all this. Christoph [1] http://www.paraview.org/Wiki/ParaView/Line_Integral_Convolution

1 0

Spin
by Alexis Bozio June 26, 2015

June 26, 2015

Hello, I'm trying to calculate transmission function including spin with Matrix for onsite values but when i am writting the code that is explained on the site (http://kwant-project.org/doc/1.0/tutorial/tutorial2) it makes the calculation but a few seconds later Python stops and all the datas vanishe. Thank you for your help. Best Regards. Alexis Bozio

2 5

Effective Hamiltonian with leads
by Gerson June 19, 2015

June 19, 2015

I would like to either get the local Green's function at a single site of my system with the effect of the leads included. The Green's function method of Kwant does not give me this, right? But I could get I want combining the system Hamiltonian if the leads self- energy: Heff = Hsys + Sigma However, "sys.hamiltonian_submatrix()" gives me the full Hsys, while "sys.leads[0].selfenergy(energy=0.01)" gives me only the submatrix of lead interface. How can I reshape the self-energy to obtain the Heff? Once I have Heff, I can calculate the GF via Geff = [w - i.eta - Heff]^{-1} Then, how can I access the local GF of a given site? Geff[lat(i,j)]? Best, Gerson

1 0

site potential
by Sebastian June 19, 2015

June 19, 2015

Dear All, is there a way to get information on the potential of the sites? In my case every site gets a random number between -1 and 1. In a second step I would like to check whether the potentials of neighboring sites differ too much and if they do, reset their potenials. Thank You in advance, Sebastian

2 3