Mailman 3 April 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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Re: [Kwant] How to caculate hall resistance
by Anton Akhmerov April 28, 2014

April 28, 2014

> Thank you very much for your help. But I have two questions about your > advice. One question is why we need to correct digonal element to make rows > and columns sum to zero? Do you mean digonal element of conductance matrix > is not well defined? The transmission, as returned by Kwant is just the norm of the corresponding block of the scattering matrix. In order to get the conductance matrix from that, one needs to subtract the number of modes from the diagonal entries. This is achieved by the line cond -= np.diag(cond.sum(axis=0)) in the code snippet that I sent. > Another question is why we need to eliminate one row > and one column? Can we just solve np.linalg.solve(cm, [1, 0, -1,0]) to get > V_1,V_2,V_3,V_4, where cm is 4x4 conductance matrix. The conductance matrix has a zero eigenvalue, so the solution to the full problem is not unique (you can add a constant to every potential, and currents won't change). On the other hand, the currents are not independent, since the total current has to equal to zero. Eliminating a row and a column takes care of both constraints. Best, Anton > > Best Regards, > Zhang Bing > > > on 2014/4/27 21:03, Anton Akhmerov wrote: >> >> Dear Zhang Bing, >> >> Please take a look at the following bit of code that calculates >> nonlocal resistance in a 4-terminal device from a Kwant scattering >> matrix. (Taken from the Kwant example to appear with the revised >> version of Kwant paper.) >> >> # First we calculate the conductance matrix given the scattering >> matrix S. >> cond = np.array([[s.transmission(i, j) for j in xrange(n)] for i in >> xrange(n)]) >> # Correct the reflection blocks, so that rows and columns sum to >> zero. >> cond -= np.diag(cond.sum(axis=0)) >> >> # In order to calculate the nonlocal conductance we eliminate one row >> and >> # one column from the condutcance matrix. This amounts to setting the >> # corresponding voltage to zero and using current conservation to >> calculate >> # the current through the last terminal. >> cm = conductance_matrix(sys, energy, [args])[:-1, :-1] >> # We then set the current to be 1 in the lead 0, -1 in lead 2, and >> # calculate the voltage in lead 1 (so V_1 - V_3 since V_3 = 0). >> nonlocal_resistance = np.linalg.solve(cm, [1, 0, -1])[1] >> >> Generalization to a 6-terminal case should be straightforward. >> >> Best regards, >> Anton Akhmerov >> >> On Sat, Apr 26, 2014 at 6:14 AM, ZHANG Bing <bzhangac(a)ust.hk> wrote: >>> >>> 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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installation problem OS X Mavericks
by Sebastian Huber April 24, 2014

April 24, 2014

When trying to install kwant on OS X Mavericks I get the following error: -=[*]=-/usr/local/Cellar$ brew install tinyarray ==> Downloading http://downloads.kwant-project.org/tinyarray/tinyarray-1.0.2.tar Already downloaded: /Library/Caches/Homebrew/tinyarray-1.0.2.tar.gz Warning: Formula#python is deprecated and will go away shortly. ==> python setup.py install --prefix=/usr/local/Cellar/tinyarray/1.0.2 Error: can't convert PythonDependency into String Please report this bug: https://github.com/Homebrew/homebrew/wiki/troubleshooting /usr/local/Library/Homebrew/formula.rb:531:in `basename' /usr/local/Library/Homebrew/formula.rb:531:in `system' /usr/local/Library/Taps/michaelwimmer-kwant/tinyarray.rb:11:in `install' /usr/local/Library/Homebrew/build.rb:174:in `install' /usr/local/Library/Homebrew/formula.rb:267:in `brew' /usr/local/Library/Homebrew/formula.rb:587:in `stage' /usr/local/Library/Homebrew/resource.rb:62:in `unpack' /usr/local/Library/Homebrew/extend/fileutils.rb:21:in `mktemp' /usr/local/Library/Homebrew/resource.rb:59:in `unpack' /usr/local/Library/Homebrew/resource.rb:52:in `stage' /usr/local/Library/Homebrew/formula.rb:585:in `stage' /usr/local/Library/Homebrew/formula.rb:262:in `brew' /usr/local/Library/Homebrew/build.rb:151:in `install' /usr/local/Library/Homebrew/build.rb:45:in `main' /usr/local/Library/Homebrew/build.rb:12 /usr/local/Library/Taps/michaelwimmer-kwant/tinyarray.rb:10 I get the same error with the apple python as well as with the homebrew one. Any suggestions? Thank you Sebastian

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3D structure construction
by Shicheng Lu April 15, 2014

April 15, 2014

Hi, I am trying to construct a 3D SrTiO3 structure, however there is only one example in online document that is 3D. I can create the structure and attach two leads, but I am not sure how to define the hopping energy between atoms. Here is how I create the 3D structure by using lattice.general: lat = kwant.lattice.general([(0, 0, 1),(0, 1, 0), (1, 0, 0)], [(0, 0, 0),(0.5,0.5,0),(0.5,0,0.5),(0,0.5,0.5), (0.5,0.5,0.5)]) a,c1,c2,c3,b = lat.sublattices sys = kwant.Builder() sys[lat.shape(cuboid_shape, (0, 0, 0))] = 4 * t The last code is how I define the energy for the atoms, but I am not sure how to define the hopping energy between atoms here, because there are 8 1/8 Ti, 6 1/2 O and 1 Sr in this unit cell, what kind of function should I use here? Best, Shicheng Lu Department of Physics & Astronomy University of Pittsburgh

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launch the kwnat.test()
by Loïc Maury April 7, 2014

April 7, 2014

Hello, I am new to the project, and I try to launch the first test. Unfortunately when I do : python -c 'import kwant; kwant.test()', that doesn't work : *ImportError: cannot import name lapack* but I have already installed liblapack-dev, I'am on Debian. Thank you Loic

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TSC/TI
by Ian R George April 3, 2014

April 3, 2014

Hello, I am an undergraduate student who is new to KWANT and condensed matter physics as a whole. I was wondering if anyone had some code meant to simulate the tight binding model for a topological insulator or superconductor, or could point me in the right direction? I have a paper that is helping me systematically construct the Hamiltonian analytically for different classes of TI's and TSC's, but I'm finding it hard to code. Maybe I just don't understand it well enough. I'm sorry if I'm stating something dumb or trivial. Thank you for your time.

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