Mailman 3 January 2022 - Kwant-discuss

Defining uniaxial strain in specified region of graphene
by shrushti.tapar07＠gmail.com 20 Jan '23

20 Jan '23

I want to create the graphene strained superlattice-like structure, having uniaxial strain defined at the specified region. Please, someone can suggest to me how to define the strained region and interface between unstrained and strained graphene regions. Thanks in Advance Shrushti

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Gate-defined Nanowire Quantum Dot
by Jonathan Fields 15 Sep '22

15 Sep '22

Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gate-defined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/cond-mat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wrap-around' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a source-drain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>

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current-voltage diagram
by loojoo026＠gmail.com 08 Apr '22

08 Apr '22

dear all I have done my project using Kwant and I have drawn a conductance-energy diagram for the system. The question I have is how can I get the current-voltage diagram? thanks Leo

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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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Spin polarized transport calculation
by L.M J 06 Mar '22

06 Mar '22

Dear Kwant users and developers I have two questions related to the spin calculation using kwant. 1. I'm wondering if we can do spin-polarized transport in kwant? For example, can we can get the separate Conductance Vs Energy diagram for spin up and spin down terms. I'm thinking one way of doing this is to set up the Rashba Hamiltonian as a whole. And then manually extract the spin up and spin down hamiltonian and do the transport calculation separately. But this will eliminate some extra terms that I don't know whether this is correct anymore. Any suggestions? 2. How can we set up the spin polarization for a particular site? For example, in some of the topological insulator, can we set up spin polarization on the edge as up and the other side of the edge as down, and then do the transport? Or this question is completely wrong? Thanks for advance. Sincerely, Liming

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Parallel Computation
by diegobruno244＠gmail.com 04 Mar '22

04 Mar '22

Kwant Community, I would like to know if it is possible to do parallel computing using kwant? To do parallel computing can be used numba, CUDA, multiprocessing, Parallel. This work for kwant? And if possible are there any examples?

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Graphene Conductor-Superconductor Conductance above Gap
by Henry Axt 21 Feb '22

21 Feb '22

Hello, I set up a graphene lattice with periodic boundary conditions that is connected to a superconductor (simulated with an electron and hole lattice). When observing the transmission between the electron and hole lattice, I see a small amount conductance above the superconducting gap. I do not see this with something like a square lattice. What could explain this?

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Surprising (?) behaviour of attach leads
by maciej.zwierzycki＠ifmpan.poznan.pl 15 Feb '22

15 Feb '22

Dear Kwant Authors and Users, Greetings and thank you for a wonderful tool. While trying to force Kwant to accept the unit cell of the lead in a particular, connected form, I've encountered somewhat puzzling situation illustrated in the attached piece of code. The described procedure does not make sense physically, but its purpose is to illustrate the behaviour which may possibly (?) lead to problems, at least for newbies like me. ;) Let's say I define two honeycomb lattices, differing in the choice of basis, but entirely equivalent (i.e. they overlap) prime=np.array([[sqrt(3)/2,sqrt(3)],[1.5,0.0]])*a basis_at=np.array([[0.0,0.0],[-0.5,0.5]])*a lat = kwant.lattice.general([prime[:,0],prime[:,1]],[basis_at[:,0],basis_at[:,1]]) and basis2=np.array([[0.0,sqrt(3)/2],[-0.5,-1.0]])*a lat2 = kwant.lattice.general([prime[:,0],prime[:,1]],[basis2[:,0],basis2[:,1]]) I'm using numpy so that vector algebra works. The rectangular scattering region and the left lead (same width) are populated with "lat". Now I'm adding a few atoms from lat2 to the right edge of the scattering region, e.g. a single hexagon for i in range (0,1): # changing the range we can generate also the full layer of lat2 sites syst[lat2.sublattices[0](0+2*i,9-i)]=0.0 syst[lat2.sublattices[1](0+2*i,8-i)]=0.0 syst[lat2.sublattices[0](1+2*i,8-i)]=0.0 syst[lat2.sublattices[1](1+2*i,8-i)]=0.0 and then attach the lead, also populated with "lat2". I know, that's not how it's described in tutorial. ;) The filling algorithm generates the system which to naked eye looks like the perfect nanowire. The transmission however is not perfect i.e. T < N (number of modes). If the full layer of lat2 sites is added to the right edge, than everything is as it should be, i.e. perfect transmission. I'm not sure if it's a bug - I'm doing things not in the manual - but I find it strange. A perfect system, however generated, should lead to perfect transmission. What gives? Also I noticed that neighbours() method called for one of the lattices tends to pick up the sites from the other lattice, if they belong to he sublattice generated from (0,-0.5a), i.e. from the common basis. Try commenting out one of the lines 53-54. Is it intentional or not? It's quite likely that the described situation never arises in real-world situations especially if one does the right thing and pads the interface with the full principal layer before attaching the leads. I've stumbled upon it only thanks to my laziness. But it might also illustrate some fragility of the algorithm, possibly worth eliminating. In any case I'd be grateful for some illumination. Why isn't the "perfect" wire behaving as it should? Where is the imperfection if it's not visible in the structure? With Kind Regards Maciej Zwierzycki import kwant import numpy as np from numpy import sin, cos,tan,sqrt from matplotlib import pyplot def make_system(a, t, W, L1): prime=np.array([[sqrt(3)/2,sqrt(3)],[1.5,0.0]])*a basis_at=np.array([[0.0,0.0],[-0.5,0.5]])*a lat = kwant.lattice.general([prime[:,0],prime[:,1]],[basis_at[:,0],basis_at[:,1]]) syst = kwant.Builder() #### Define the scattering region. #### def scatt_shape(pos): (x, y) = pos return (-L1 < x < L1) and ( -W <y < W) syst[lat.shape(scatt_shape,basis_at[:,0])]=0 syst[lat.neighbors()] = t #### Left lead. #### def lead_shape(pos): (x, y) = pos return (-W < y < W ) lsym=kwant.TranslationalSymmetry(lat.vec((0,-1))) lsym.add_site_family(lat.sublattices[0], other_vectors=[(-2,1)]) lsym.add_site_family(lat.sublattices[1], other_vectors=[(-2,1)]) llead = kwant.Builder(lsym) llead[lat.shape(lead_shape,basis_at[:,0])] = 0 llead[lat.neighbors()] = t #### Right lead. #### ### Define a hexagonal lattice with different - but equivalent! - basis basis2=np.array([[0.0,sqrt(3)/2],[-0.5,-1.0]])*a lat2 = kwant.lattice.general([prime[:,0],prime[:,1]],[basis2[:,0],basis2[:,1]]) #### Extra hexagon of lat2 on the right edge of the scattering region: #### -- range(0,1) - single hexagon ##### -- range(-2,3) - full width for i in range (0,1): syst[lat2.sublattices[0](0+2*i,9-i)]=0.0 syst[lat2.sublattices[1](0+2*i,8-i)]=0.0 syst[lat2.sublattices[0](1+2*i,8-i)]=0.0 syst[lat2.sublattices[1](1+2*i,8-i)]=0.0 syst[lat2.neighbors()]=t syst[lat.neighbors()]=t kwant.plot(syst) lsym=kwant.TranslationalSymmetry(lat2.vec((0,1))) lsym.add_site_family(lat2.sublattices[0], other_vectors=[(2,-1)]) lsym.add_site_family(lat2.sublattices[1], other_vectors=[(2,-1)]) rlead= kwant.Builder(lsym) rlead[lat2.shape(lead_shape,basis_at[:,0])] = 0 rlead[lat2.neighbors()] =t syst.attach_lead(llead) syst.attach_lead(rlead) syst=syst.finalized() return syst syst = make_system(a=1.42,t=3.0,W=10.5,L1=20) kwant.plot(syst) data1 = [] data2 = [] params = dict(a=1.42, t=-3.0) energies=[0.2*i+0.01 for i in range(20)] for energy in energies: print('En=',energy) smatrix = kwant.smatrix(syst, energy,params=params) data1.append(smatrix.transmission(1, 0)) data2.append(smatrix.num_propagating(0)) pyplot.figure() pyplot.plot(energies, data1, 'r--', label='T') pyplot.plot(energies, data2,'r>', label='N') legend = pyplot.legend(loc='upper left') pyplot.xlabel("energy") pyplot.ylabel("conductance [e^2/h]") pyplot.show()

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How to attach a lead to particular position of honeycomb lattice
by sahu.ajit92＠gmail.com 04 Feb '22

04 Feb '22

Dear Sir, I am new to kwant. How to attach a lead to a particular portion(upper side of the square) of the honeycomb structure. sym1 = kwant.TranslationalSymmetry(lat.vec((0,1))) lead1 = kwant.Builder(sym1) def lead2_shape(pos): x, y = pos return 0<x<10 lead1[lat.shape(lead2_shape, (2,0))]=3 lead1[lat.neighbors()] = -1 I used the above code to attach the second lead but it didn’t attach to the correct place. I want to attach the lead to the upper side of the square. main code Wnr=10 lnr=10 a=1 lat=kwant.lattice.honeycomb(a) def rect(pos): x,y=pos return 0<x<lnr and 0<y<Wnr model1 = kwant.Builder() model1[lat.shape(rect,(1,1))] = 3 model1[lat.neighbors()] =-1 ##########lead shape function def lead1_shape(pos): x, y = pos return 0 < y < 10 def lead2_shape(pos): x, y = pos return 0<x<10 ##########1st lead########## sym = kwant.TranslationalSymmetry(lat.vec((-1,0))) #from the left sym.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)]) sym.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)]) lead = kwant.Builder(sym) lead[lat.shape(lead1_shape, (1,1))]=3 lead[lat.neighbors()] = -1 model1.attach_lead(lead) ##########problem in 2nd lead, from this below code it attach to other position########## sym1 = kwant.TranslationalSymmetry(lat.vec((0,1))) lead1 = kwant.Builder(sym1) lead1[lat.shape(lead2_shape, (2,0))]=3 lead1[lat.neighbors()] = -1 model1.attach_lead(lead1) kwant.plot(model1) Anyone, please help please see this image in below link, I want to attach the second lead in the red-circled position of the figure https://drive.google.com/file/d/15ORyo4j_tAvgC8jaT5lQxmQNS6e0QoOF/view?usp=…

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Elements of a scattering matrix
by Lorenzo BAGNASACCO 04 Feb '22

04 Feb '22

Dear Kwant community, I am a physics student and I am approaching to Kwant to solve simple problems of scattering. I am new in Kwant and, for this reason, I'm trying to use Kwnat for basic problems of scattering. The most simple problem in my mind is the scattering of a plane-wave (1 dimension) from the left of a potential barrier. If we now suppose the potential barrier is 'zero' everywhere, the scattering matrix, according to the scattering theory, should be 'S={{0,1},{1,0}}'. If I try to compute the reflection and transmission coefficient, I obtained the correct values (1 for reflection and 0 for transmission). But it occurs only for some energies. For example in the code I attached, if I put the value of '10' in 'S=kwant.solvers.default.smatrix(syst,10)' I obtaine for reflection and transmission the value of '0'. Where is my errors? And, is there a way to print the entire elements of the scattering matrix ? Yours sincerely Lorenzo Bagnasacco

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Kwant-discuss January 2022