Mailman 3 August 2020 - Kwant-discuss

Realistic values of hopping parameters
by Yu Li 18 Oct '23

18 Oct '23

Dear all, Now I’m studying some transport property based on multilayered system, with nonmagnetic layer/ferromagnetic layer (NM/FM) stack. May I ask when creating a tight binding system, and setting hoppings by the following function: syst[(lat(1, 0), lat(1, 1))] = t, how to associate the hopping with a realistic system? Such as hoppings between FM and FM atoms, or between FM and NM atoms? I found in many literatures people just simply put t=1, but I assume the value should depend on the type of atoms. My another question is, is it possible to define more than one type of hopping between two sites? For the tight-binding approximation of p electrons, there are two types of hopping integrals: Vppσ, and Vppπ, so I’m wondering if it’s possible to simulate the effect of both hoppings? Thanks a lot for reading my questions! Cheers, Yu Li

4 3

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

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

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

Kwant is taking a unit cell larger than the one defined in the calculation of the phosphorene band structure
by Ronan Viana 27 Aug '20

27 Aug '20

Hi, colleagues! I'm defining the phosphorene unit cell perfectly. However, when the leads are attached to the scattering region, the kwant increases the unit cell, and thus "duplicate" energy levels appear. I'm using the model with 10 interlayer hoppings and 5 interlayer hoppings. Apparently, in the model of 5 interlayer hoppings it doesn't happen! Thank you for your help now.

3 3

Periodic and open boundary conditions
by Deepti Rana 26 Aug '20

26 Aug '20

Hi, I am trying to calculate the conductance through coupled quantum nanowires. I have basically considered a square lattice with hopping tx in x direction and modulating the coupling between the wires through ty i.e. the hopping in y direction. My system requires periodic boundary condition along x direction and open boundary condition in y direction. Can you please help me in how this can be done using kwant to meet the above boundary conditions. I have mentioned my code below. Since I am new to Kwant, it would be of much help to me if you help me solving this. Regards Deepti Rana def make_sys1(a=1,W=4,barrierpos=1): def onsite_normal(site,p): return( (2 * (p.tx+p.ty) - p.mu) * pauli.s0sz+p.Ez*pauli.szs0)) def onsite_sc(site,p): return (2 * (p.tx+p.ty ) * pauli.s0sz+p.Ez*pauli.szs0)+p.delta*pauli.s0sx) def onsite_barrier(site,p): return((2*(p.tx+p.ty)+ p.Vbarrier-p.mu)*pauli.s0sz+p.Ez*pauli.szs0)) def hopx(site1, site2, p): return -p.tx * pauli.s0sz +1j* p.alphax * pauli.sysz def hopy(site1, site2, p): return -p.ty * pauli.s0sz -1j * p.alphay * pauli.sxsz lat = kwant.lattice.square(a,norbs=4) syst = kwant.Builder() syst[(lat(x, y) for x in range(barrierpos) for y in range(W))]=onsite_barrier syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy sym_left = kwant.TranslationalSymmetry((-a, 0)) lead0 = kwant.Builder(sym_left, conservation_law=-pauli.s0sz) lead0[(lat(0, j) for j in range(W))]=onsite_normal lead0[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx lead0[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy sym_right = kwant.TranslationalSymmetry((a, 0)) lead1 = kwant.Builder(sym_right) lead1[(lat(0, j) for j in range(W))]=onsite_sc lead1[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx lead1[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy syst.attach_lead(lead0) syst.attach_lead(lead1) syst = syst.finalized() return syst

2 1

Andreev reflection in graphene
by Martin Fonnum Jakobsen 26 Aug '20

26 Aug '20

Hi, this is a follow up question to a previous (hijacked?) thread. For completeness I will provide all details, so that no cross referencing is necessary. I want to compute the electrical conductance of a N-S interface embedded on a hexagonal lattice. The final result should look something like the picture I have attached. The BdG equation is specified in the .pdf. At the moment I have both particle-hole and spin-up/down degrees of freedom, because later I want to add magnetic fields and such. To attack the problem I have tried to follow the steps outlined in tutorial 2.6 with the addition that I use 4 orbitals and a hexagonal lattice. The conductance should still be given as N - R_{ee,\uparrow} - R_{ee,\downarrow} + R_{he,\uparrow} + R_{he,\downarrow}. Here e, h, \uparrow, and \downarrow refers to electron, hole, spin-up, and spin-down respectively. In the documentation it says that smatrix.transmission((i, a), (j, b)) gives the transmission from block b of lead j to block a of lead i. I would therefore expect smatrix.transmission((0, 2), (0, 0)) to give me the transmission of an incident electron of spin up in lead 0 to a reflected hole of spin up in lead 0. With this in mind I thought I could write data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0]- smatrix.transmission((0, 0), (0, 0)) - smatrix.transmission((0, 1), (0, 0)) + smatrix.transmission((0, 2), (0, 0)) + smatrix.transmission((0,3), (0, 0))) to compute the conductance. However, doing this gives me an out of bounds error. As a last resort I tried to write data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] - smatrix.transmission((0, 0), (0, 0)) + smatrix.transmission((0, 1), (0, 0))) as given in the tutorial 2.6. However, this gives me that the conductance is zero. My question is then, how do I correctly interpret the smatrix.transmission function in my example so that I can compute the correct conductance? I have attached my code in the .txt file. Best, Martin

1 0