Kwant-discuss September 2015

kwant-discuss@python.org

22 participants
33 discussions

How the spin is positioned in the Smatrix?
by Qingtian Zhang 06 Mar '22

06 Mar '22

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 12 Sep '21

12 Sep '21

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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New instructions for Windows installation
by Michael Wimmer 15 Jan '16

15 Jan '16

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

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QZ Iteration fails
by Maximilian Trescher 09 Nov '15

09 Nov '15

Dear kwant users and developers, this is my first post to this list, I'm a PhD student from Berlin. Currently I'm trying to implement a lattice model of a pyrochlore slab in kwant. I found a (more or less straightforward) way to introduce periodic boundary conditions in the system in the maillinglist archive. This works very nicely as long as I keep the periodicity along a lattice vector. But I run into problems when I choose different directions: Most of the time all solvers fail with a "LinAlgError: QZ iteration failed to converge in zgges". I know about this post http://comments.gmane.org/gmane.comp.science.kwant.user/372 but in my case it occurs not only for a band bottom, but for a range of energies. To give you all the details I prepared a Ipython notebook that you can view here: http://nbviewer.ipython.org/gist/faucon/729050da5e3f2eae1bb8# (Note that the inclusion of complex next-nearest-neighbor hopping is crucial to produce the error, I tried to create the shortest example which reproduces my problem). Do you have any idea how to circumvent this problem? Is it somehow related to http://netlib.org/lapack/Errata/vrac/lapack_known_issues.html#QZ this problem in Lapack? I would be thankful for any hint, Best, Maximilian

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ldos.cumsum or ldos.cumprod
by Dedi Setiabudidaya 29 Sep '15

29 Sep '15

Hi there, I tried the functions ldos.cunsum() and ldos.cumprod() and succeeded in obtaining the plot;but I do not know what the plots told me. Anyone can help ?Below is the codes for the plot data1 = []energies = np.linspace(1,4,101)for energy in energies: ldos = kwant.ldos(sys,energy) data1.append(ldos.cumsum())pyplot.figure()pyplot.plot(energies, data1)pyplot.xlabel("energy [t]")pyplot.ylabel("ldos")pyplot.show() and for the other plot I just changed the function ldos.cumsum() with ldos.cumprod(). Thank you in advance. Kind Regards, Dedi

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Scotch/MUMPS from source vs from repositories
by Baris Pekerten 29 Sep '15

29 Sep '15

Dear all, Is there a significant speed difference between MUMPS/scotch from Ubuntu repos vs. from source, especially considering that Kwant uses only the single core algorithms? Latest MUMPS in the Ubuntu repos is 4.10. Latest stable release of MUMPS is 5.0.5. I try to install everything from source. Speed is an issue for me. (Last work I did involved ~2M runs of a 4x4 hamiltonian defined on a 4x60000 wire with random potential per plot, which took ~16 days per plot with the computational power available to me.) However, it's easy (for me) to have a MUMPS installation go wrong, so I'd rather install them from repos unless there's a significant speed advantage. Thank you for your time and concern, Baris

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kkghosh
by kamal ghosh 29 Sep '15

29 Sep '15

Dear all, Please help me in correcting the following program which I tried to mimic a portion of the program on transmission through a quantum well. I tried the following: import kwant import cmath lat=kwant.lattice.square(1) sys=kwant.Builder() def potential(site,pot): (x,y)=site.pos if 10 < x< 20: return pot else: return 0 def onsite(site,pot=0): return potential(site,pot) print potential(12,0) Error shown : (x,y)=site.pos; there is no attribute in int (x,y)= site.pos It is strange that in the original program of the quantum well, I also could not explain why that program run successfully! because there also no such "pos" attribute is defined anywhere. Please bear with my misunderstanding and rectify me with brief tutorial. K.K.Ghosh mail: kk_ghosh(a)rediffmail.com

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Dynamic number of lattices
by Baris Pekerten 29 Sep '15

29 Sep '15

Dear all, I need to calculate a system with a variable number of 2D lattices. So, the pseudo code should look like: for i in xrange(2,100): # Form a system with (i) number of lattices, with hoppings that depend on (i) in between the lattices # Calculate stuff, such as the transmission amplitude from lead f of lattice j to lead g of lattice k (j, k <= i) # plot calculated stuff as a function of i I couldn't figure out a straight method to do it, as I have to pass (i) as a function variable when I'm forming the hoppings. That is, in the make_system part of the code, I need to say things like (again in pseudo code) syst[(lat(i, x, y), lat(i+1, x, y) for x in ... for y in ...)] = hopping(i, i+1) which is impossible because a) lattice definitions can only take in realspace coordinates and b) the function on the right side has to have two sites as its first two arguments and the rest will be provided in the solver part of the code. I found two rather inelegant possible solutions to my problem. (I'm trying only the second one). What I'm asking is, is there a better solution? Inelegant (and possibly wrong) solution 1: Make this a truly 3D rectangular prism system, with each layer corresponding to one lattice. This makes the problem of writing the hoppings trivial, but then how would I get the transmission amplitude from the left lead of 2D lattice number 35 to the right lead of 2D lattice number 67? Inelegant solution 2: Code-generating code. This is what I've done. Essentially, I generate a .py file with 100 copies of the make_system function, each with different number of lattices. Later, in the main code, I import the appropriate make_system function from this .py file and solve my system. Thank you all for your time and concern. Cheers, Baris P.

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Re: [Kwant] Problem with elements of S-matrix not being smooth
by Anton Akhmerov 28 Sep '15

28 Sep '15

Hi Simon, > This helps a lot!! I think it may also help others to mention this in the > tutorial somewhere if it doesn't already. (Apologies, I may have missed it). Good idea, do you have a specific place in mind where this remark could go? You're welcome to submit corrections to the documentation. Also if you find a good recipe for uniquely fixing the phase, please share it on the mailing list. Best, Anton PS Greetings to Henning > Thank you and best wishes, > > Simon > > On Mon, Sep 28, 2015 at 6:58 PM, Anton Akhmerov <anton.akhmerov(a)gmail.com> > wrote: >> >> Hi Simon, >> >> Kwant algorithms do not adapt any particular convention in choosing >> the phases of the modes in the leads. That's why the scattering matrix >> at different energies can be discontinuous. You can access the wave >> functions of the modes through the resulting smatrix [1]. You can also >> easily modify the way Kwant calculates modes like we've done in [2]. >> >> Hope that helps, >> Anton >> >> [1]: >> http://kwant-project.org/doc/1.0/reference/generated/kwant.solvers.common.S… >> [2]: http://arxiv.org/abs/1408.1563 specifically >> http://arxiv.org/src/1408.1563v2/anc/trijunction.py >> >> >> On Mon, Sep 28, 2015 at 7:41 PM, Simon Malzard <smalzard01(a)gmail.com> >> wrote: >> > Hello Kwant, >> > >> > The problem I am trying to solve relies on being able to calculate the >> > eigenphases of the scattering matrix for different energies, more >> > precisely >> > it requires the elements of the scattering matrix to be smooth as a >> > function >> > of energy. >> > >> > By examining the elements of the scattering matrix as a function of >> > energy, >> > I have noticed that the elements of the scattering matrix are not smooth >> > and >> > there exists a sign problem. >> > >> > The code I have included below is for a highly(!!) simplified example, >> > where >> > the scattering region is simply two leads attached to a single square. I >> > took the base code from the kwant tutorial page to reduce any possible >> > errors. I have taken a small range of energies and plotted the real >> > parts of >> > the off diagonal elements of the scattering matrix. You will notice that >> > plot included demonstrates that the elements of the scattering matrix >> > are >> > not smooth and a sign change occurs for certain energies (sign changes >> > for >> > both the real and imaginary parts, plotting chosen for simplicity). >> > >> > Note that for the example I take a tiny range of energies, where the >> > conductance is the same and hence the number of active modes is constant >> > as >> > a function of energy. >> > >> > There may be a mistake in understanding on my part, however, I believe >> > this >> > error is due to some sign error in the incoming or outgoing states in >> > the >> > lead as this only effects individual modes (as you will see when you >> > adjust >> > the system size, or move up to the next conductance plateau and the size >> > of >> > the scattering matrix increases. My initial program was looking at >> > graphene >> > for a large rectangular flake and I noticed this effect considerably). I >> > think this is a boundedness problem for certain functions which >> > describes >> > the individual scattering states at certain energies. >> > >> > Is this intentional behaviour for KWANT? As it means I can't perform >> > calculations such as calculating the Wigner-Smith time-delay matrix, >> > among >> > other scattering characteristics. >> > >> > Thank you for your time + best wishes, >> > >> > Simon >> > >> > >> > My code: >> > >> > >> > #### KWANT tutorial code >> > from matplotlib import pyplot as plt >> > import kwant >> > import numpy as np >> > import scipy.linalg as la >> > # First, define the tight-binding system >> > >> > sys = kwant.Builder() >> > >> > # Here, we are only working with square lattices >> > a = 1 >> > lat = kwant.lattice.square(a) >> > >> > t = 1.0 >> > W = 2 >> > L = 2 >> > >> > # Define the scattering region >> > >> > for i in xrange(L): >> > for j in xrange(W): >> > # On-site Hamiltonian >> > sys[lat(i, j)] = 4 * t >> > >> > # Hopping in y-direction >> > if j > 0: >> > sys[lat(i, j), lat(i, j - 1)] = -t >> > >> > # Hopping in x-direction >> > if i > 0: >> > sys[lat(i, j), lat(i - 1, j)] = -t >> > >> > # Then, define and attach the leads: >> > >> > # First the lead to the left >> > # (Note: TranslationalSymmetry takes a real-space vector) >> > sym_left_lead = kwant.TranslationalSymmetry((-a, 0)) >> > left_lead = kwant.Builder(sym_left_lead) >> > >> > for j in xrange(W): >> > left_lead[lat(0, j)] = 4 * t >> > if j > 0: >> > left_lead[lat(0, j), lat(0, j - 1)] = -t >> > left_lead[lat(1, j), lat(0, j)] = -t >> > >> > sys.attach_lead(left_lead) >> > >> > # Then the lead to the right >> > sym_right_lead = kwant.TranslationalSymmetry((a, 0)) >> > right_lead = kwant.Builder(sym_right_lead) >> > >> > for j in xrange(W): >> > right_lead[lat(0, j)] = 4 * t >> > if j > 0: >> > right_lead[lat(0, j), lat(0, j - 1)] = -t >> > right_lead[lat(1, j), lat(0, j)] = -t >> > >> > sys.attach_lead(right_lead) >> > >> > # Plot it, to make sure it's OK >> > kwant.plot(sys) >> > >> > # Finalize the system >> > sys = sys.finalized() >> > >> > # Now that we have the system, we can compute conductance >> > >> > emin, emax = 1.05, 1.06#3.00 >> > points = 21 >> > >> > energies = np.linspace(emin,emax,points) >> > element_0_1, element_1_0 = [], [] >> > >> > for ie in energies: >> > >> > energy = ie >> > # I only consider element 0,1 and 1,0 as 0,0 and 1,1 are vanishingly >> > small and look like floating point errors. >> > >> > #This gets the smartix and looks at the real parts of the >> > off-diagonal >> > elements >> > smatrix = kwant.smatrix(sys, energy).data >> > element_0_1.append(smatrix[0,1].real) >> > element_1_0.append(smatrix[1,0].real) >> > >> > print smatrix[0,1].real >> > print smartix[1,0].real >> > >> > fig2 = plt.figure() >> > ax2 = fig2.add_subplot(1,1,1) >> > ax2.plot(element_0_1, 'ro') >> > ax2.plot(element_1_0, 'bo') >> > plt.show() >> > > >

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Re: [Kwant] Site ordering while plotting wavefunction
by Anton Akhmerov 28 Sep '15

28 Sep '15

> I was wondering if there is some link which explains how to put hoppings for > a 3D system. The general procedure: sys[lat(i, j, k), lat(i - 1, j, k)] = > -t doesn't seem to work and gives an error: Polyatomic object not callable. You seem to be using a lattice with more than one sublattice, check out the graphene tutorial (kwant-project.org/doc/1.0/tutorial/tutorial4.html). Otherwise 3D isn't different from 2D. Best, Anton > Thank you and regards, > Girish > > On Sun, Sep 27, 2015 at 8:53 AM, Anton Akhmerov <anton.akhmerov(a)gmail.com> > wrote: >> >> Dear Girish, >> >> See the example of plotting an 1D wave function over here: >> >> http://nbviewer.ipython.org/github/topocm/topocm_content/blob/master/w1_top… >> >> Best, >> Anton >> >> On Fri, Sep 25, 2015 at 9:16 PM, Girish Sharma <girishs(a)g.clemson.edu> >> wrote: >> > Hi, >> > >> > I have attached a small code, trying to visualize Majorana wavefunctions >> > at >> > the two end points of my 1D wire. The kwant.plotter doesn't really help, >> > so >> > I'm trying basic pyplot. However, due to random ordering of sites, I do >> > not >> > see the wavefunction peaking at the ends (see the last plot). Is there a >> > way >> > out to do this ordering correctly in PYTHON? >> > >> > Thank you for your time ! >> > >> > Best regards, >> > Girish > >

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Kwant-discuss September 2015