Mailman 3 August 2017 - Kwant-discuss

Gate-defined Nanowire Quantum Dot
by Jonathan Fields Sept. 15, 2022

Sept. 15, 2022

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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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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Spin polarized transport calculation
by L.M J March 6, 2022

March 6, 2022

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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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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Current in a closed system
by Abbout Adel Oct. 26, 2017

Oct. 26, 2017

Dear All, I was consulting the example of the current in a *closed system* and I am a little bit confused: The figure showing the current flowing inside a circle [1] is obtained for a magnetic field B=0 ! But we know that for B=0, the Hamiltonian is a real symmetric matrix and thus diagonalized by a real orthogonal matrix, so the eigenvectors are real (any phase is just artificial.) By using the formula giving the current we should find zero ! moreover we can ask why we have a current flowing clockwise and not anticlockwise (I remind that B=0) ! When we put B=0.05, we obtain the figures below for the current and the wave function. the wave function has circular symmetry but not the current. Moreover, x and y play exactly the same role so the current should be the same on x and on y (independently from the used gauge) Am I missing something ? Thank you in advance. Adel [1] https://kwant-project.org/doc/1/tutorial/spectrum

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lead_info
by Prof. CHAN Kwok Sum Sept. 20, 2017

Sept. 20, 2017

Dear Kwant developer, Thank you for your effort in developing Kwant. I have a question about the definition of the direction of momentum in the smatrix.lead_info. Assume a lead lies along the y direction with primitive vector (0,1). The symmetry operation of a lead is (0,1) if the lead goes towards the positive direction and is (0,-1) if the lead goes towards the negative direction. For the momenta contained in smatrix.lead_info for these two leads , do they use the same coordinate system? Positive momenta mean the direction (0,1), negative momenta mean the direction (0,-1). For velocity, in smatrix.lead_info, it has nothing to do with the coordinate system. Positive means outgoing, negative means incoming in the lead. Thank you KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

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2D Current Density Streamplot of 3D System
by Mitchell Greenberg Sept. 16, 2017

Sept. 16, 2017

Hello, I am currently completing my thesis using Kwant, per discussions with my supervisor we would like to plot the current density as a streamplot of our 3d system for different z-axis 'slices' of the system (our system has an exponentially decaying potential in the z direction, so we'd expect current to flow differently through each layer). I have tried tinkering with the new current functions implemented in 1.3 but the plotting function can only plot 2d systems. Is there a way to obtain the current density streamplot for a 2d 'slice' of our 3d system. Thank You, Mitchell Greenberg

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superconductivity and current conservation
by Tibor Sekera Aug. 31, 2017

Aug. 31, 2017

Dear all, in the tutorial https://kwant-project.org/doc/1/tutorial/superconductors one calculates the conductance from left lead to right lead, G_10, as G_00 = e^2/h (N-R_ee+R_he) assuming that, due to the current conservation, G_10 = G_00. My question is, what happens if we detach the superconducting lead L1. Intuitively, I would expect G_00 = 0. But using the formula above one obtains non-zero values, and making the finite superconducting region (the part of the scattering region) large enough, the subgap transport is exactly as if the lead L1 was attached. This means that the current conservation is violated, and something is wrong. Below is slightly modified code from the tutorial to generate a plot comparing G_00 for a system with and without lead L1. You can see, that if parameter L (the superconducting part of the scattering region) is large enough, the subgap transport is the same whether L1 is attached or not. Why is this happening, can someone point out the error? Best, Tibor import kwant import tinyarray import numpy as np %matplotlib inline from matplotlib import pyplot as plt tau_x = tinyarray.array([[0, 1], [1, 0]]) tau_y = tinyarray.array([[0, -1j], [1j, 0]]) tau_z = tinyarray.array([[1, 0], [0, -1]]) L=80 barrier=1.5 W=10 def make_system(a=1, W=W, L=L, barrier=barrier, barrierpos=(3, 4), mu=0.4, Delta=0.1, Deltapos=4, t=1.0, phs=True): lat = kwant.lattice.square(norbs=2) syst = kwant.Builder() syst[(lat(x, y) for x in range(0,Deltapos) for y in range(W))] = (4 * t - mu) * tau_z syst[(lat(x, y) for x in range(Deltapos, L) for y in range(W))] = (4 * t - mu) * tau_z + Delta * tau_x # The tunnel barrier syst[(lat(x, y) for x in range(barrierpos[0], barrierpos[1]) for y in range(W))] = (4 * t + barrier - mu) * tau_z # Hoppings syst[lat.neighbors()] = -t * tau_z sym_left = kwant.TranslationalSymmetry((-a, 0)) lead0 = kwant.Builder(sym_left, conservation_law=-tau_z, particle_hole=tau_y) lead0[(lat(0, j) for j in range(W))] = (4 * t - mu) * tau_z lead0[lat.neighbors()] = -t * tau_z sym_right = kwant.TranslationalSymmetry((a, 0)) lead1 = kwant.Builder(sym_right) lead1[(lat(0, j) for j in range(W))] = (4 * t - mu) * tau_z + Delta * tau_x lead1[lat.neighbors()] = -t * tau_z syst.attach_lead(lead0) syst.attach_lead(lead1) return syst syst = make_system() kwant.plot(syst) syst = syst.finalized() data = [] energies=[0.002 * i for i in range(0,100)] for energy in energies: smatrix = kwant.smatrix(syst, energy) # Conductance is N - R_ee + R_he data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] - smatrix.transmission((0, 0), (0, 0)) + smatrix.transmission((0, 1), (0, 0))) syst = make_system() del syst.leads[-1] # Check that the system looks as intended. kwant.plot(syst) # Finalize the system. syst = syst.finalized() data2 = [] for energy in energies: smatrix = kwant.smatrix(syst, energy) # Conductance is N - R_ee + R_he data2.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] - smatrix.transmission((0, 0), (0, 0)) + smatrix.transmission((0, 1), (0, 0))) fig , (ax0) = plt.subplots(1, 1, sharey = True, figsize = [5, 5]) ax0.plot(energies, data, label = 'with lead 1') ax0.plot(energies, data2, label = 'without lead 1') ax0.set_xlabel("energy [t]") ax0.set_ylabel("conductance [e^2/h]") ax0.set_ylim(0,3.5) ax0.legend() fig.savefig('NS_conductance.png')

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lead self energy
by Chung Tsai Aug. 31, 2017

Aug. 31, 2017

Dear kwant community, I am new in Transport and kwant. I have two simple questions regarding the lead, I appreciate any reply. 1-The lead's self energy is in principle a complex number. In kwant, If I want to add the self energy of a lead by hand, I can add the real part of it to the on-site energy of the site that lead is connected to. Where should I add the imaginary part of the self energy? 2- If I know the value of the level width function (\Gamma = 2πρt^2 = 1), and the lead is a 1D chain, can I calculate the value of the coupling parameter, t? Is there a way to obtain the DOS of the lead and then get t? Bests Chung

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continuous vs discrete leads
by Patrik Arvoy Aug. 25, 2017

Aug. 25, 2017

Dear kwant users, If I want to attach a continuous lead instead of its discrete counterpart to a discrete system, I get the error message 'Use site_family(1, 2) instead of site_family((1, 2))!'. The discrete lead is according to the following prim_vecs=tinyarray.array([(a,0.,0.),(0.,a,0.),(0.,0.,a)]) offset1=tinyarray.array((-0.7, 0.0, 0.0)) lat1=kwant.lattice.Monatomic(prim_vecs, offset1, norbs=no) syst[lat1(0, 0, -1)] = e1*sigma_0 syst[amorphous_lat(0), lat1(0, 0, -1)] = tl*sigma_0 syst[amorphous_lat(N), lat1(0, 0, -1)] = tl*sigma_0 sym = kwant.TranslationalSymmetry([0, 0, -a]) dn_lead = kwant.Builder(sym, conservation_law=-sigma_z) if discrete: sym = kwant.TranslationalSymmetry([0, 0, -a]) dn_lead = kwant.Builder(sym, conservation_law=-sigma_z) dn_lead[lat1(0, 0, -2)] = e1*sigma_0 dn_lead[lat1.neighbors()] = t0*sigma_0 syst.attach_lead(dn_lead) Now if I replace the 'if discrete:' part with the following if continuous: t00=0.0 Leadham = "t00*sigma_0*k_x**2+t00*sigma_0*k_y**2-t0*sigma_0*k_z**2+(2*t0+e1)*sigma_0" template = kwant.continuum.discretize(Leadham grid_spacing=a) dn_lead.fill(template, lat1, lat1(0, 0, -2)) syst.attach_lead(dn_lead) I have to add k_x and k_y with zero coefficient (t00) to solve the symmetry complain (is there a neater way?) where is the error message ('Use site_family(1, 2) instead of site_family((1, 2))!') originated from? Thanks Patrik

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