Mailman 3 April 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))

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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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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

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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

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Re: [Kwant] Kwant-discuss Digest, Vol 18, Issue 1
by Lee Kwok-Long May 23, 2015

May 23, 2015

Dear Joe, Thanks, it is very useful for me. I want to know more about how the transmission is related to the wave vector kx, because I want to calculate the transmission contributed from some scale like kx=0~pi. So, how can i know the wave vector for "2" in S10[3, 2] ? I tried "modes = Smatrix.lead_info", it seems that it does not give the kx information. I can take graphene as an example, we have two valleys K and K' in graphene. Since the wave vectors kx for the two valleys are different, we can calculate the transmission contributed from K valley and K' valley separately, but of course we need to know "transmission-mode-kx" first. Maybe this can be easily solved in another way. Kwok-Long Lee On Fri, Feb 6, 2015 at 8:03 PM, <kwant-discuss-request(a)kwant-project.org> wrote: > Send Kwant-discuss mailing list submissions to > kwant-discuss(a)kwant-project.org > > To subscribe or unsubscribe via the World Wide Web, visit > https://mailman-mail5.webfaction.com/listinfo/kwant-discuss > or, via email, send a message with subject or body 'help' to > kwant-discuss-request(a)kwant-project.org > > You can reach the person managing the list at > kwant-discuss-owner(a)kwant-project.org > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Kwant-discuss digest..." > > > Today's Topics: > > 1. Transmission of each propagating mode (Lee Kwok-Long) > 2. Re: Transmission of each propagating mode (Joseph Weston) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Fri, 6 Feb 2015 16:43:23 +0800 > From: Lee Kwok-Long <kwoklonglee(a)gmail.com> > To: kwant-discuss(a)kwant-project.org > Subject: [Kwant] Transmission of each propagating mode > Message-ID: > < > CAMzfLzK0z7uFZGB54o71i8yr0hb2hf1D9GXxEhckubFYuQC5_g(a)mail.gmail.com> > Content-Type: text/plain; charset="utf-8" > > Dear all, > I want to calculate the transmission of each propagating mode separately, > but I do not know how the propagating modes are related to the scattering > matrix. For example, we can read from the bandstructure and find a mode at > E=0.2，kx=0.95pi, how to find the transmission for this mode. Or, we have > the transmission and how to find the contributions from each mode? Thanks > in advance! > Kwok-Long Lee >

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attaching 1D lead to 2D lattice
by Sergey May 2, 2015

May 2, 2015

Dear Colleagues, I want to measure the decay of wave-function in magnetic field. For that I create a 2D shape and want to attach a 1D lead to only one internal lattice site of a 2D shape. (imagine, that this 1D chain is pointing in the third direction, although this embedding does not matter for physics) Does this make sense? There is a technical problem that 1D families differ from 2D ones and I get a message: "ValueError: Sites with site families (kwant.lattice.Monatomic([[1.0]], [0.0], ''),) do not appear in the system, hence the system does not interrupt the lead." <mailto:kwant-discuss@kwant-project.org> Any hints? Thank you, Sergey

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suggestion
by Sergey April 30, 2015

April 30, 2015

Dear Authors, It would be convenient to improve the method kwant.lattice.Monatomic.n_closest to include an argument "range" or even two arguments: range_min = 0 and range_max so that it returns the sites within a range from the given point. This is useful to e.g. specify the hoppings between incommensurate lattices. Thanks, Sergey

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what is the wave function inside the system?
by Mariya Medvedyeva April 29, 2015

April 29, 2015

Thanks a lot for you package which is rather intuitive in using! Could you please help with understanding of the wave function which KWANT gives? I could not understand what kwant.wave_function gives as an output: -- how to distinguish between the modes which are propagating in the leads and which are decaying in the leads? kwant.wave_function gives an answer at any energy. (1)For example, how do get the density in some transport setup? Is this example correct? def Fermi(energy, T, mu): f = 1./(1. + math.exp ( (energy - mu) / T) ) return f def density(sys,energy,lead_nr): wf = kwant.wave_function(sys,energy) return (abs(wf(lead_nr))**2).sum(axis=0) numleads = 2 Tmu = numpy.array([[Tleft,muleft],[Tright,muright]]) #assuming that this range of energies encompasses well the chemical potential range de = 0.05 nenergies = 100 energies=[de * (i - nenergies/2) for i in xrange(nenergies)] for energy in energies: for num_lead in xrange(numleads): d = d + Fermi(energy, Tmu[num_lead]) * density(sys, energy, num_lead) d = d * de (2) Another example which I do not understand properly is about transport through a translationally invariant 2d bar. >From physical reasoning, I would expect that the current through each link in the direction of the current is the same. So I tried to apply the formula (11) from the NJP-introduction to KWANT. But I get a very different looking answers, comparing to scattering matrix approach, as well as current throught different links in the direction of the current is different. Why are these two answers so different and one is not oscillating, and another is so much depends on energy? (In 1d the comparission works well) def Fermi(energy, T, mu): f = 1./(1. + math.exp ( (energy - mu) / T) ) return f #potentials in the leads muleft = -2. muright = 2. mu = 0 Tleft = 0.1 Tright = 0.1 #potentials and temepratures of all leads muTAll = [] muTAll.append([muleft,Tleft]) muTAll.append([muright,Tright]) energies = [] data = [] nenergies = 300 de = 0.032424 CurrentWave = [] CurrentLandauer = [] t = 1. W = 6 L = 10 numleads = 2 numsite = (L-1)* W sys = BuildSystem(t, W, L,mu,mu,mu) #beginning and end of stm link in terms of program; x=[] for i1 in xrange(numsite): x.append(sys.sites[i1].pos) beg=[] for i1 in xrange(numsite): if x[i1] == [1,1]: beg.append(i1) end=[] for i1 in xrange(numsite): if x[i1] == [2,1]: end.append(i1) print beg, end for imu in xrange(1): sysFinal = BuildSystem(t, W, L, mu, mu, mu) for ienergy in xrange(nenergies): energy = de * ienergy - nenergies * de / 2. energies.append(energy) wf = kwant.wave_function(sysFinal,energy) smatrix = kwant.smatrix(sysFinal, energy) #wave function based calculation which can be used for any correlation function #iterating over number of leads wfInside = numpy.zeros(numsite) #wave function inside of the system for p in xrange( numleads): wave = wf(p) lenwave = wave.shape [0] for ipsi in xrange(lenwave): wfInside = wfInside + Fermi(energy, muTAll[p][1],muTAll[p][0] ) * wave[ipsi] ProbeCurrent = wfInside[beg] * wfInside[end].conjugate() - wfInside[end] * wfInside[beg].conjugate() CurrentWave.append( ProbeCurrent[0].imag) #Getting wave function is done #transmission based calculation t10 = smatrix.transmission(1, 0) data.append(t10) t2 = t10 * (Fermi(energy, muTAll[1][1],muTAll[1][0] ) - Fermi(energy, muTAll[0][1],muTAll[0][0] )) CurrentLandauer.append(t2) plt.figure() plt.plot(energies, CurrentLandauer) plt.plot(energies, CurrentWave) plt.xlabel("energy [t]") plt.ylabel("conductance [e^2/h]") plt.show() def BuildSystem(t, W, L, mu, muleft, muright): sys = kwant.Builder() #DEFINING THE SYSTEM a=1. lat = kwant.lattice.square(a) for i in xrange(L-1): for j in xrange(W): sys[lat(i,j)] = mu if j > 0: sys[lat(i,j), lat(i,j-1)] = -t if i > 0: sys[lat(i,j), lat(i-1,j)] = -t #ATTACHING LEADS #lead is pointing away from scattering region sym_left_lead = kwant.TranslationalSymmetry((-a,0)) left_lead = kwant.Builder(sym_left_lead) for j in xrange(W): left_lead[lat(0,j)] = muleft if j > 0: #modeling large band-width in the leads, that is why 10. t left_lead[lat(0,j), lat(0,j-1)] = - t left_lead[lat(1,j), lat(0,j)] = - t sys.attach_lead(left_lead) sym_right_lead = kwant.TranslationalSymmetry((a,0)) right_lead = kwant.Builder(sym_right_lead) for j in xrange(W): numx = L-2 right_lead[lat(numx,j)] = muright if j > 0: #modeling large band-width in the leads, that is why 10. t right_lead[lat(numx,j), lat(numx,j-1)] = - t right_lead[lat(numx,j), lat(numx+1,j)] = - t sys.attach_lead(right_lead) sysFinal = sys.finalized() t2 = time.clock() return sysFinal

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Appcrash for very large systems
by Sam LaGasse April 28, 2015

April 28, 2015

Greetings all, I have a question regarding using kwant for very large systems. In my research I am trying to model graphene-based devices on the order of L = W = 500 nm. I encounter a problem when trying to simulate electron density in these devices with Kwant. The errors I get look like this: Faulting application name: python.exe, version: 0.0.0.0, time stamp: 0x5488acd7 Faulting module name: _mumps.pyd, version: 0.0.0.0, time stamp: 0x54d2a92a Exception code: 0xc00000fd Fault offset: 0x000000000076e357 Faulting process id: 0x5018 Faulting application start time: 0x01d0811ecc4f2ba7 Faulting application path: C:\WinPython-64bit-2.7.9.4\python-2.7.9.amd64\python.exe Faulting module path: C:\WinPython-64bit-2.7.9.4\python-2.7.9.amd64\lib\site-packages\kwant\linalg\_mumps.pyd Report Id: d70446a6-ed26-11e4-9806-b8ac6f4eb471 A little info on the system: I am running 64 bit python installed from the WinPython package. The IDE is Spyder. I've gotten all of the example codes to work as well as several of my own (albeit for smaller versions of the systems we would like to study). >From the error and doing some testing with the code, I've devised that it must be a problem occuring solver itself. I have enough memory to build the system and I am pretty sure I am not running out of memory during the actual solving, although I am not positive. I am wondering if the mumps routine could be breaking for very large systems? When I run my code on a laptop with much less ram (~60 gb for the desktop vs 4 gb on the laptop) I end up with a memory error instead of a kernel crash. I've attached a modified version of one of the tutorial codes, where I have added in a LDOS/electron density calculation and increased the dimensions of the simulation to 500x1000. The code successfully finalizes the device on my machine, but crashes the python kernel during the actual calculation. I can get more ram for the machine if necessary, but I want to make sure that it isn't a problem related to the solver before sending the purchase order to my advisor. Kwant seems extremely nice so we're hoping to use it in our research in the future! It is a lot better than the NEGF code I strung together in matlab! Thank you! Sam LaGasse

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Re: [Kwant] Formation of Hamiltonian with Rashba Interaction with up and down spin
by Sudin Ganguly April 28, 2015

April 28, 2015

Dear Sir, Thank you for the reply. The main motivation of my question was ---- How the Hamiltonian of the scattering region is going into the 'sys'? If I want to check the Hamiltonian with the help of Hamiltonian_submatrix(), from the output matrix I am unable to understand how the onsite and hopping terms are positioned in that matrix. I read the post about 'Site position in hamiltonian matrix', but still I'm not getting this. With regards, Sudin

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