Mailman 3 January 2018 - 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

combine two kwant.plotter.current figures into a single one
by Tibor Sekera 05 Feb '18

05 Feb '18

Dear all, sorry, this might be more a matplotlib question than a kwant question. Below is a minimal code which produces two figures, each showing a different dataset: a current in the scattering region due to a wavefunction in a lead. I would like to combine the two into a single plot, distinguishing the two datasets by e.g. different colormaps (and two different colorbars). Any ideas? Thanks a lot, Tibor ______________________________________ import kwant from math import pi, sqrt from cmath import exp import numpy from matplotlib import pyplot as plt #some parameters t=1 L=30 W=30 EF=0.1 phi=0.01 def hopping(sitei, sitej, phi): xi, yi = sitei.pos xj, yj = sitej.pos return -t*exp(1j*2*pi*phi*2/sqrt(3)*(yj - yi)*(xi + xj)/2) def make_system(): lat = kwant.lattice.general([(sqrt(3)*1/2, 1/2), (0, 1)], [(0, 0), (1/(2*sqrt(3)),1/2)], norbs=1) def central_region(pos): x, y = pos return abs(x) < L/2 and abs(y) < W/2 def lead0_shape(pos): x, y = pos return abs(x) < L/2 #scattering region sys = kwant.Builder() sys[lat.shape(central_region, (0,0))] = -EF sys[lat.neighbors()] = hopping sys.eradicate_dangling() #leads sym = kwant.TranslationalSymmetry(lat.vec((0,1))) lead0 = kwant.Builder(sym) lead0[lat.shape(lead0_shape, (0,0))] = -EF lead0[lat.neighbors()] = hopping lead0.eradicate_dangling() lead1=lead0.reversed() return sys, lead0, lead1 sys, lead0, lead1 = make_system() sys.attach_lead(lead0) sys.attach_lead(lead1) sysf = sys.finalized() wf = kwant.wave_function(sysf, energy=0.0001, params=dict(phi=phi)) J = kwant.operator.Current(sysf) psi1 = wf(0)[0] e_current1 = J(psi1, params=dict(phi=phi)) psi2 = wf(1)[0] e_current2 = J(psi2, params=dict(phi=phi)) kwant.plotter.current(sysf, e_current1, cmap="OrRd", colorbar=True, show=False) ax = plt.gca() plt.colorbar(ax.get_children()[-2], ax=ax) kwant.plotter.current(sysf, e_current2, cmap="Blues", colorbar=True, show=False) ax = plt.gca() plt.colorbar(ax.get_children()[-2], ax=ax) plt.show()

3 3

Building tight binding Hamiltonian with multi atom with multi-orbital basis
by Santu Baidya 30 Jan '18

30 Jan '18

Dear Kwang users, I have recently started using Kwant for making model Hamiltonian. It is really very good python package. I have started learning some tutorials. I would like to know if making tight-binding Hamiltonian with multi atom and multi orbital basis possible using Kwant. I can not find such example in documentation. I would like to then try to make a honeycomb lattice with two atoms and each atom with two basis, e.g., px, py. Please help me to know about this in more detail. Thanking you, Santu B Sent from my iPad

4 6

Arbitrary spin polarization for the incident wave
by Wei Chen 23 Jan '18

23 Jan '18

Hi all, I am working on a spin resolved scattering problem using Kwant. The setup is a simple heterojunction composed of normal metal and spin-orbit coupled systems. I want to calculate the probabilities of spin-flipped and spin-conserved reflection. In the normal metal, I use two lattices for spin-up and spin-down states, and the calculation went well. The probabilities for spin-flipped and spin-conserved reflection can be read through inter- and intra-lattice scattering. Now I want to calculate the scattering problem for an incident wave with spin polarization in the x-direction. My question: how to set the incident spin state along the x-direction and calculate the corresponding spin-flipped (spin in -x direction) and spin-conserved scattering probabilities? Thanks very much! Best, Wei -- College of Science, University of Aeronautics and Astronautics, Nanjing, 210016, P. R. China E-mail: pchenweis(a)gmail.com <pchenweis(a)163.com>, weichenphy(a)nuaa.edu.cn

2 2

getting less number of peaks in transmission for 1D chain
by SUDIN GANGULY 23 Jan '18

23 Jan '18

Dear Sir, Recently I was doing a problem on a 1D chain. The problem I faced is as follows. For a 1D chain, suppose I have taken 5 sites and set the hopping strength between lead and system very small compared to the system hopping. Now since we have 5 sites, from the Hamiltonian of the system we'll have 5 eigenvalues and if we calculate the transmission coefficient we shall have 5 peaks each occurs at particular eigenvalue. But in my case, I am getting only three peaks. Am I missing something here? Please help me. The following code I have used for the transmission calculation. #===================CODE================== import kwant # For plotting from matplotlib import pyplot import numpy as np def make_system(a=1, t=1.0, L=5): # Start with an empty tight-binding system and a single square lattice. # `a` is the lattice constant (by default set to 1 for simplicity. lat = kwant.lattice.chain(a) syst = kwant.Builder() #### Define the scattering region. #### for x in range (L): syst[(lat(x))] = 0 #syst[(lat(x) for x in range(L))] = onsite syst[lat.neighbors()] = -t #### Define and attach the leads. #### lead = kwant.Builder(kwant.TranslationalSymmetry([-a])) lead[(lat(0))] = 0 lead[lat.neighbors()] = -t syst.attach_lead(lead) syst.attach_lead(lead.reversed()) #============== set hopping between lead and system ============ for i in syst.leads[0].interface: for j in syst.neighbors(i): syst[i,j] = 0.1 for i in syst.leads[1].interface: for j in syst.neighbors(i): syst[i,j] = 0.1 return syst #================================================================ def main(): syst = make_system() # Check that the system looks as intended. kwant.plot(syst) # Finalize the system. syst = syst.finalized() Es = np.linspace(-1.99, 1.99, 800) data = [] totdos = [] for e in Es: smatrix = kwant.smatrix(syst, e) T = smatrix.transmission(1, 0) ldos = kwant.ldos(syst, e) totdos.append(sum(ldos)/len(ldos)) data.append(T) print ('%0.3f' % e, '%.4f' % T, sum(ldos)/len(ldos)) pyplot.figure() pyplot.plot(Es, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main() #================End CODE======================= -- সুদিন

3 2

V-I curves in Kwant
by Shivang Agarwal 12 Jan '18

12 Jan '18

Hi All, I am trying to plot V-I curves for graphene quantum dots but don't know how to proceed. I have plotted conductance as a function of energy. Can anyone help me understand how do I obtain V-I curves? Any help will be much appreciated! Thank you, Sincerely, Shivang -- *Shivang Agarwal* Junior Undergraduate Discipline of Electrical Engineering IIT Gandhinagar Contact: +91-9869321451

1 0

Energy dispersion of MoS2
by Gongwei_Hu 03 Jan '18

03 Jan '18

Dear all Kwant workers! My problem is about the calculation of energy dispersion of MoS2 in Ref PRB 92, 195402 (2015). I want to use the tight binding Hamiltonian of MoS2 (Eq (2) in Reference) to obtain energy dispersion in Figure 6(a). Because the honeycomb of monolayer MoS2 is distinct with the graphene, onsite energy of Mo and S is also different. In graphene, the onsite energy of A and B atoms in unit cell is equivalent and thus the hopping energy of nearest and two nearest atom in different direction is same. However, this is not right in MoS2 (A----Mo, B----S). So i choose the code to describe onsite energy in MoS2 as follow def onsite(site): return E_M if (site.family == M) else E_X Is this right? Furthermore, i solve the energy band in y-direction by considering only one lead (abs(y)<Ly, Ly is the width). Is it correct to use the following code to build the system? sym = kwant.TranslationalSymmetry(lat.vec((-1, 0))) sys = kwant.Builder(sym) My Kwant code cannot obtain the result in Figure 6(a). Please help me if you are free, Thanks! My Kwant code: import kwant from matplotlib import pyplot import tinyarray import math import numpy eV, nm=1,1e-9 lamad_M, lamad_X = 0.075*eV, 0.052*eV e0, e2, ep, ez = -1.094*eV, -1.512*eV, -3.560*eV, -6.886*eV V_pdd, V_pdp = 3.689*eV, -1.241*eV V_ddd, V_ddp, V_ddde = -0.895*eV, 0.252*eV, 0.228*eV V_ppd, V_ppp = 1.225*eV, -0.467*eV; a0=0.316*nm; s=1j; sz=+1; sqrt_3=math.sqrt(3) E_M=tinyarray.array([[e0, 0, 0],[0, e2, -s*lamad_M*sz],[0, s*lamad_M*sz, e2]]); E_X=tinyarray.array([[ep+V_ppp, -s*lamad_X/2*sz, 0],[s*lamad_X/2*sz, ep+V_ppp, 0],[0, 0, ez-V_ppd]]); t1_MX=1/7*math.sqrt(2/7)*tinyarray.array([[-9*V_pdp+sqrt_3*V_pdd, 3*sqrt_3*V_pdp-V_pdd, 12*V_pdp+sqrt_3*V_pdd], [5*sqrt_3*V_pdp+3*V_pdd, 9*V_pdp-sqrt_3*V_pdd, -2*sqrt_3*V_pdp+3*V_pdd], [-V_pdp-3*sqrt_3*V_pdd, 5*sqrt_3*V_pdp+3*V_pdd, 6*V_pdp-3*sqrt_3*V_pdd]]) t2_MX=1/7*math.sqrt(2/7)*tinyarray.array([[0, -6*sqrt_3*V_pdp+2*V_pdd, 12*V_pdp+sqrt_3*V_pdd], [0, -6*V_pdp-4*sqrt_3*V_pdd, 4*sqrt_3*V_pdp-6*V_pdd], [14*V_pdp, 0, 0]]) t3_MX=1/7*math.sqrt(2/7)*tinyarray.array([[9*V_pdp-sqrt_3*V_pdd, 3*sqrt_3*V_pdp-V_pdd, 12*V_pdp+sqrt_3*V_pdd], [-5*sqrt_3*V_pdp-3*V_pdd, 9*V_pdp-sqrt_3*V_pdd, -2*sqrt_3*V_pdp+3*V_pdd], [-V_pdp-3*sqrt_3*V_pdd, -5*sqrt_3*V_pdp-3*V_pdd, -6*V_pdp+3*sqrt_3*V_pdd]]) t1_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3/2*(-V_ddde+V_ddd), -3/2*(V_ddde-V_ddd)], [sqrt_3/2*(-V_ddde+V_ddd), 1/4*(V_ddde+12*V_ddp+3*V_ddd), sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd)], [-3/2*(V_ddde-V_ddd), sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd), 1/4*(3*V_ddde+4*V_ddp+9*V_ddd)]]) t2_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3*(V_ddde-V_ddd), 0], [sqrt_3*(V_ddde-V_ddd), V_ddde+3*V_ddd, 0], [0 , 0,4*V_ddp]]) t3_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3/2*(-V_ddde+V_ddd), 3/2*(V_ddde-V_ddd)], [sqrt_3/2*(-V_ddde+V_ddd), 1/4*(V_ddde+12*V_ddp+3*V_ddd), -sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd)], [3/2*(V_ddde-V_ddd), -sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd), 1/4*(3*V_ddde+4*V_ddp+9*V_ddd)]]) t1_XX=1/4*tinyarray.array([[3*V_ppp+V_ppd, sqrt_3*(V_ppp-V_ppd), 0], [sqrt_3*(V_ppp-V_ppd), V_ppp+3*V_ppd,0], [0, 0, 4*V_ppp]]) t2_XX=tinyarray.array([[V_ppd, 0, 0], [0 ,V_ppp, 0], [0, 0, V_ppp]]) t3_XX=1/4*tinyarray.array([[3*V_ppp+V_ppd, -sqrt_3*(V_ppp-V_ppd), 0], [-sqrt_3*(V_ppp-V_ppd), V_ppp+3*V_ppd, 0], [0, 0 ,4*V_ppp]]) lat = kwant.lattice.honeycomb() M, X = lat.sublattices def make_lead(Lx=1, Ly=48): def Rectangle(pos): x, y = pos return abs(y)<Ly def onsite(site): return E_M if (site.family == M) else E_X #sym = kwant.TranslationalSymmetry((-Lx, 0)) #sym = kwant.TranslationalSymmetry((-3, 0)) sym = kwant.TranslationalSymmetry(lat.vec((-1, 0))) sys = kwant.Builder(sym) #sys = kwant.Builder() sys[lat.shape(Rectangle, (0, 0))] = onsite #hopping_onsit_M=((0, 0),M,M) #hopping_onsit_X=((0, 0),X,X) #sys[kwant.builder.HoppingKind(*hopping_onsit_M)] = E_M########## #sys[kwant.builder.HoppingKind(*hopping_onsit_X)] = E_X######### hopping2_M =((1, 0), M, M) hopping1_M =((-1, 1), M, M) hopping3_M =((0, -1), M, M) sys[kwant.builder.HoppingKind(*hopping1_M)] = t1_MM sys[kwant.builder.HoppingKind(*hopping2_M)] = t2_MM sys[kwant.builder.HoppingKind(*hopping3_M)] = t3_MM hopping2_X =((1, 0), X, X) hopping1_X =((-1, 1), X, X) hopping3_X =((0, -1), X, X) sys[kwant.builder.HoppingKind(*hopping1_X)] = t1_XX sys[kwant.builder.HoppingKind(*hopping2_X)] = t2_XX sys[kwant.builder.HoppingKind(*hopping3_X)] = t3_XX hopping1_MX =((0, 0), M, X) hopping2_MX =((0, 1), M, X) hopping3_MX =((-1, 1), M, X) sys[kwant.builder.HoppingKind(*hopping1_MX)] = t1_MX sys[kwant.builder.HoppingKind(*hopping2_MX)] = t2_MX sys[kwant.builder.HoppingKind(*hopping3_MX)] = t3_MX def family_colors(site): return 0 if (site.family == M) else 1 def hopping_lw(site1, site2): return 0.05 if site1.family == site2.family else 0.1 def hopping_color(site1,site2): return 'g' if site1.family==site2.family else 'b' kwant.plot(sys,site_color=family_colors,site_lw=0.05, hop_lw=hopping_lw,hop_color=hopping_color,colorbar=False) return sys def main(): lead = make_lead().finalized() kwant.plotter.bands(lead, show=False) pyplot.xlabel("momentum [(lattice constant)^-1]") pyplot.ylabel("energy [eV]") pyplot.show() # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main()

2 1