Mailman 3 May 2020 - Kwant-discuss

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>

4 4

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))

3 3

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

3 3

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

4 3

To to separate spins, electron and hole
by Khani Hosein 22 Jun '21

22 Jun '21

Dear all, I am using Kwant to study a system with both spins and electron and hole, so the hopping matrix is 4X4. Now I want to know how to separate the spins, electron and hole. I study this through the "2.6. Superconductors: orbital degrees of freedom, conservation laws and symmetries" smatrix = kwant.smatrix(syst, energy) data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -smatrix.transmission((0, 0), (0, 0)) +smatrix.transmission((0, 1), (0, 0))) I do not find more information about this for kwant. For my system, if I have 3 leads, and the hopping and onsite energy is set in this order: (e↑,0,0,0)- spin up electron,first row of the 4X4matrix (0,e↓,0,0)- spin down electron,second row of the 4X4matrix (0,0, h↑ ,0)- spin up hole,third row of the 4X4matrix (0,0, 0, h ↓ )- spin down hole,fourth row of the 4X4matrix I want to obtain the transmissions from 0 →2. smatrix = kwant.smatrix(syst, energy) The transmission from h↑ to e↑ is: smatrix.transmission((2, 1), (0, 2)) The transmission from h ↓ to e↑ is: smatrix.transmission((2, 1), (0, 3)) Is my understanding correct? Thanks very much in advance! Hosein Khani

3 4

adding a scatterer with internal degree of freedom
by Ahmet Mert Bozkurt 01 Jun '20

01 Jun '20

Dear KWANT developers, I would like to add a localized magnetic impurity into a quantum spin hall system with spin-flip interaction (sigma_plus I_- + sigma_- I_+ where I is the magnetic impurity spin operator. The spin-flip interaction depends on the state of the magnetic impurity (whether it is spin-up or spin-down). If it's spin-up, it needs to interact only with the spin down electrons (term sigma_+) flip them upwards, while the magnetic impurity state needs to be updated to spin-down. I've written a code using two different lattices (lat_up and lat_down) and simply check transmission from one lattice lead to the other lattice lead. But this method becomes impractical if i want to add more magnetic impurities because i need to add more and more lattice (2^N). Is there any easier way to include a scatterer with internal degree of freedom (which can be updated perhaps using tkwant or any other way)? BTW this is the model I'm working on:https://arxiv.org/abs/1705.04985 Below is the relevant part of my code and thank you so much in advance! Mert # Scattering region syst[lat_up.shape(shape, (0, 0))] = onsite syst[lat_down.shape(shape, (0, 0))] = onsite syst[kwant.HoppingKind((1, 0), lat_up)] = hopx syst[kwant.HoppingKind((1, 0), lat_down)] = hopx syst[kwant.HoppingKind((0, 1), lat_up)] = hopy syst[kwant.HoppingKind((0, 1), lat_down)] = hopy syst[(lat_up(10, 2), lat_down(10, 2))] = 0.1*0.5*np.kron(pauli.sp, pauli.s0) syst[(lat_down(10, 2), lat_up(10, 2))] = 0.1*0.5*np.kron(pauli.sm, pauli.s0) # two lines above correspond to spin-flip of the magnetic impurity, jumping from one #lattice to the other. #### Define the leads. #### sym_left = kwant.TranslationalSymmetry((-1, 0)) lead_up = kwant.Builder(sym_left) lead_down = kwant.Builder(sym_left) lead_up[lat_up.shape(lead_shape, (0, 0))] = onsite_lead lead_down[lat_down.shape(lead_shape, (0, 0))] = onsite_lead lead_up[kwant.HoppingKind((1, 0), lat_up)] = hopx_lead lead_up[kwant.HoppingKind((0, 1), lat_up)] = hopy_lead lead_down[kwant.HoppingKind((1, 0), lat_down)] = hopx_lead lead_down[kwant.HoppingKind((0, 1), lat_down)] = hopy_lead # Attach leads syst.attach_lead(lead_up) syst.attach_lead(lead_down) syst.attach_lead(lead_up.reversed()) syst.attach_lead(lead_down.reversed()) def plot_conductance(sys, p, mu): # Compute conductance p.mu = mu data = [] smatrix = kwant.smatrix(sys, energy = 0.0, params = dict(p=p)) no_flip = smatrix.transmission(2, 0) flip = smatrix.transmission(1,0) return no_flip, flip

2 4

Kpoint-resolved transmission spectrum
by Zhou Jiaqi 26 May '20

26 May '20

Dear all, We all know that it is easy to realize the energy-resolved transmission spectrum using Kwant. I am looking for the method to realize kpoint-resolved transmission spectrum using Kwant, like the output of non-equilibrium Greens function - density functional theory (NEGF-DFT) in the following link : https://www.researchgate.net/figure/shows-that-the-features-of-k-resolved-t… I note that we can use “params” to use the selected kpoint in 'kwant_model.hamiltonian_submatrix'. Take Gamma (0, 0, 0) as an example : Input : kwant_model.hamiltonian_submatrix(params={'k_x': 0, 'k_y': 0, 'k_z': 0}) Output : (the hamiltonian at Gamma kpoint) array([[-0.91848142+0.j , -3.13863545+0.05174286j, 0.01464058-0.12995645j, 5.49753359+1.2518773j ], [-3.13863545-0.05174286j, -0.91858637+0.j, -5.63827375-0.00282617j, 0.01464063-0.1299569j ], [ 0.01464058+0.12995645j, -5.63827375+0.00282617j, -0.91851442+0.j , -3.13862945+0.05174286j], [ 5.49753359-1.2518773j , 0.01464063+0.1299569j , -3.13862945-0.05174286j, -0.91857308+0.j ]]) Then after diagonalization we can get eigenvalues at Gamma point and k-resolved band. I wonder if we can use this method to get k-resolved transmission spectrum. I tried the following instruction : kwant.smatrix(kwant_model, params={'k_x': 0, 'k_y': 0, 'k_z': 0}) However, it does not work, i.e., the output does not vary with different kpoint (I am sure it should vary in physics). So here is the question: how to (maybe use ‘params’ in SMatrix) study transport at different kpoint using Kwant? Any suggestions will be greatly appreciated, thanks a lot! Sincerely, Jiaqi

2 4

Kwant parallelization
by Zhou Jiaqi 25 May '20

25 May '20

Hi everyone, I am writing to discuss the parallelization of Kwant. I installed Kwant with MUMPS from Ubuntu(https://launchpad.net/ubuntu/+source/mumps). When I run a Kwant script (which will be shown in the end) in the normal way on a 4-core laptop (2 threads per core), the screenshot (the output of htop, see https://drive.google.com/open?id=1TwEuc21DMjRnVQ9yG3XpkVilhFiAKaeb) shows that all the 8 CPU threads are involved, but 21 python threads. However, according to the tutorial: " Kwant uses only the sequential, single core version of MUMPS. The advantages due to MUMPS as used by Kwant are thus independent of the number of CPU cores of the machine on which Kwant runs.” So it confuses me whether Kwant 1.4.1 has already employed parallelization or not, and why there are 21 python threads? Moreover, I find the usage of concurrent package slows down the calculation. Thanks a lot for your time, and it would be greatly appreciated if anyone could share some news about the Kwant parallelization development. Best regards, Jiaqi UCLouvain ______________________ import kwant import tbmodels import numpy as np import matplotlib.pyplot as plt model = tbmodels.Model.from_wannier_files( hr_file='graphene_hr.dat', wsvec_file='graphene_wsvec.dat', xyz_file='graphene_centres.xyz', win_file='graphene.win', h_cutoff=0.01) lattice = model.to_kwant_lattice() wire = kwant.Builder() def shape(p): x, y, z = p return -5 < x < 5 and -5 < y < 5 and -1 < z < 1 wire[lattice.shape(shape, (0, 0, 0))] = 0 model.add_hoppings_kwant(wire) sym_lead_x = kwant.TranslationalSymmetry(lattice.vec((-2, 0, 0))) lead_x = kwant.Builder(sym_lead_x) def lead_shape(p): x, y, z = p return -5 <= x <= 5 and -5 < y < 5 and -1 < z < 1 lead_x[lattice.shape(lead_shape, (0, 0, 0))] = 0 model.add_hoppings_kwant(lead_x) wire.attach_lead(lead_x) wire.attach_lead(lead_x.reversed()) syst = wire.finalized() def trans(energy): smatrix = kwant.smatrix(syst, energy) data = smatrix.transmission(1, 0) return data def main(): energies = np.linspace(0, 1, 100) tc = map(trans, energies) # transmission coefficient te = zip(energies, tc) lte = list(te) print(lte) if __name__ == '__main__': main()

3 6

discontinuity between lead and scattering region
by Naveen Yadav 20 May '20

20 May '20

Dear KWANT Developers, I am trying to plot the current density. The procedure is straightforward. I have attached leads to the scattering region (leads have same onsite and hopping as of the scattering region) as *sys[(lat(z,y,x) for z in range(H) for y in range(W)for x in range(L))]=onsitesys[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingzsys[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingysys[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingxlead=kwant.Builder(kwant.TranslationalSymmetry((1,0,0)))lead[(lat(z,y,x) for z in range(H) for y in range(W)for x in range(L))]=onsitelead[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingzlead[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingylead[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingxsys.attach_lead(lead, add_cells=80)sys.attach_lead(lead.reversed())* [image: image.png] As you can see from the plot there is a discontinuity in the plot at (W=20). Why it is so even if the scattering region and leads have same onsite and hopping and there is translation symmetry throughout ? -- Best Regards, Naveen Yadav Research Scholar Department of Physics & Astrophysics University Of Delhi New Delhi-110007

3 8

Applicability of Kwant to time-dependent gating of a TMDC quantum dot
by tiessen2＠uic.edu 18 May '20

18 May '20

To whom it may concern, I am a graduate student at the University of Illinois at Chicago (UIC) and I am interested in studying qubit manipulation in single and double quantum dots made from TMDCs. Specifically, I am interested in simulating a type of qubit/quantum dot configuration which was proposed in the following paper: https://iopscience.iop.org/article/10.1088/1367-2630/ab5ac9 I noticed that Kwant does seem to allow for time-dependent electric fields in its calculations but I wasn't sure if it could handle this specific type of problem. What I would like to know is the following: 1. Is Kwant capable of simulating a quantum dot similar to the one proposed in the linked paper 2. If not, what kind of modifications would I need to make to the code to make it possible for it to accurately simulate the proposed structure Thank you for your time, John Tiessen

4 5

Kwant-discuss May 2020