Mailman 3 August 2019 - 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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Difference between hop[0].tag and hop[1].tag
by Adel Belayadi Sept. 10, 2019

Sept. 10, 2019

Dear users, Good day. My query is about hoppings. In fact, sometimes we have to change the onsite parameters when for instance a magnetic field is applied. What is the difference between hop[0].tag and hop[1].tag My second question the onsite fuction for example: def onsite(site, V):return V why it depends on site where the shape functions for example def circle(pos): rsq = pos[0] ** 2 + pos[1] ** 2 depends on pos Best A BELAYADI

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help conda
by 白春旭 Sept. 10, 2019

Sept. 10, 2019

Dear Sir, I have a problem to install Kwant when download the Pre-built packages ( Anaconda package ). That is to say I can't download the package. My operating systems is Microsoft Windows. Can you help me. Best regards, Chunxu Bai

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Wavefunction for 2D NISIN
by Tidjani, Hanifa Sept. 3, 2019

Sept. 3, 2019

I am trying to plot the wavefunction for a 2D NISIN Hamiltonian however I am unable to get a result, this is my code: import kwant import tinyarray as ta import numpy as np import matplotlib.pyplot as plt from tqdm import tqdm import winsound import os from datetime import datetime import scipy.sparse.linalg as sla sig_0 = np.identity(4) s_0 = np.identity(2) s_z = np.array([[1., 0.], [0., -1.]]) s_x = np.array([[0., 1.], [1., 0.]]) s_y = np.array([[0., -1j], [1j, 0.]]) tau_z = ta.array(np.kron(s_z, s_0)) tau_x = ta.array(np.kron(s_x, s_0)) tau_y = ta.array(np.kron(s_y, s_0)) sig_z = ta.array(np.kron(s_0, s_z)) tau_zsig_x = ta.array(np.kron(s_z, s_x)) tau_zsig_y = ta.array(np.kron(s_z, s_y)) # Lorentzian definition def lorentzianxy(x, y, ind,y0): gam = 3 L = params["L"] #if 0<ind<L: return gam ** 2 /( gam ** 2 + (x - ind) ** 2 + (y - y0) ** 2) # else : # return 0 # Define potential def potential(site, pot,ind,y0): (x, y) = site.pos return pot * lorentzianxy(x,y,ind,y0) # Make system def makeNISIN2D(params): # List all the params W=params["W"] L=params["L"] pot = params["pot"] ind = params["ind"] mu=params["mu"] B=params["B"] Delta=params["Delta"] alpha=params["alpha"] t=params["t"] barrier = params["barrier"] Smu = params["Smu"] def lorentzianxy(x, y, ind,y0): gam = 3 L = params["L"] #if 0<ind<L: return gam ** 2 /( gam ** 2 + (x - ind) ** 2 + (y - y0) ** 2) # else : # return 0 # Define potential def potential(site, pot,ind,y0): (x, y) = site.pos return pot * lorentzianxy(x,y,ind,y0) # if y < lorentzian(x,ind)*4: # # return (tru_pot) # else: # return 0 # def Straightpotential(site, pot,ind): (x, y) = site.pos if x == ind: return pot else: return 0 def onsiteSc(site, pot,ind,y0): #(x,y)=site.pos #L=params["L"] # if x>L/2: return (4 * t - Smu) * tau_z + B * sig_z + Delta * tau_x - potential(site, pot,ind,y0)*tau_z # else: #return (4 * t ) * tau_z + B * sig_z + Delta * tau_x - potential(site, pot,ind,y0)*tau_z def onsiteNormal(site, pot,ind,y0): return (4 * t - mu) * tau_z #- potential(site, pot,ind,y0)*tau_z def onsiteBarrier(site, pot,ind,y0): return (4 * t - mu + barrier) * tau_z #- potential(site, pot,ind,y0)*tau_z def hop_x(site, pot, ind,y0): return -t * tau_z + 0.5j * alpha * tau_zsig_y def hop_y(site, pot, ind,y0): return -t * tau_z - .5j * alpha * tau_zsig_x # On each site, electron and hole orbitals. lat = kwant.lattice.square(norbs=4) syst = kwant.Builder() # S syst[(lat(i, j) for i in range(1,L-1) for j in range(W))] = onsiteSc barrierLen = 1; # I's syst[(lat(i, j) for i in range(barrierLen) for j in range(W))] = onsiteBarrier syst[(lat(i, j) for i in range(L-barrierLen, L)for j in range(W))] = onsiteBarrier syst[kwant.builder.HoppingKind((1, 0), lat, lat)]= hop_x syst[kwant.builder.HoppingKind((0, 1), lat, lat)]= hop_y # N's lead = kwant.Builder(kwant.TranslationalSymmetry((-1,0)), conservation_law=-tau_z#, particle_hole=tau_y ) lead[(lat(0, j) for j in range(W))] = onsiteNormal lead[kwant.builder.HoppingKind((1, 0), lat, lat)]= hop_x lead[kwant.builder.HoppingKind((0, 1), lat, lat)]= hop_y syst.attach_lead(lead) syst.attach_lead(lead.reversed()) return syst def sorted_eigs(ev): evals, evecs = ev evals, evecs = map(np.array, zip(*sorted(zip(evals, evecs.transpose())))) return evals, evecs.transpose() params = dict(mu=0.3, Delta=.1, alpha=.8, t=1.0, barrier = 2.0, pot = 0.0,W = 5, L = 30, ind = 0, B = 0.3, Smu=0.00,y0=0) sys = makeNISIN2D(params) sys = sys.finalized() # Calculate the wave functions in the system. ham_mat = sys.hamiltonian_submatrix(sparse=True, params = params) evals, evecs = sorted_eigs(sla.eigsh(ham_mat.tocsc(), k=20, sigma=0)) # Plot the probability density of the 10th eigenmode. kwant.plotter.map(sys, np.abs(evecs[:, 9])**2, colorbar=False, oversampling=1) And the error I get is this: "ValueError: The number of sites doesn't match the number of provided values." When I print the values they indeed are more than what they should be. I've tried a couple of things but I'm quite at a loss of what to do. I want to plot the wavefunction so I can see the Majoranas at the edges of the superconductor so that I can see how they respond to a local perturbation in the potential. Any tips would be very helpful. Kind regards, Hanifa

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How to feed a portion of a finite system to kwant.plotter.interpolate_density
by Hadi Zahir Aug. 18, 2019

Aug. 18, 2019

Dear Kwant developers, I have a finalized closed system ''sys_f'' for which I computed the local charge densities "ch_densities", which is basically a vector of length=len(sys_f.sites). For complexity reason, I'd like to feed a slice of sys_f to the interpolate_density() as: >> kwant.plotter.interpolate_density(syst=sys_p, density=ch_densities_p) where sys_p is a slice of sys_f and ch_densities_p is the corresponding density vector.Could you please let me know how to do it? Best regards,Hadi

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Hopping settings
by Khani Hosein Aug. 16, 2019

Aug. 16, 2019

Dear developers, I constructed Lat_A and Lat_B for a system. A1,A2=Lat_A.sublattices B1,B2=Lat_B.sublattices I want to set hoppings between Lat_A and Lat_B, and the hoppings are dependent on the site position.Every atom of Lat_A is coupled to all the atoms in Lat_B. Now I have tried it like this : def coupling(site1,site2): xp1,yp1=site1.pos xp2,yp2=siye2.pos return t*sqrt((xp1-xp2)**2+(yp1-yp2)**2)/d for i in range(100): for j in range(100): sys[kwant.builder.HoppingKind(( i, j), A1, B1)] = coupling sys[kwant.builder.HoppingKind(( i, j), A1, B2)] = coupling sys[kwant.builder.HoppingKind(( i, j), A2, B1)] = coupling sys[kwant.builder.HoppingKind(( i, j), A2, B2)] = coupling It can not work because it take too long to do the calculations. I am considering a bilayer system but rotations are considered, for example a twisted bilayer graphene. Could you please help me to solve this problem? Regards, Hosein Khani

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3D annulus cylinder
by Naveen Yadav Aug. 13, 2019

Aug. 13, 2019

Dear KWANT developers, I want to generate a 3D annulus cylinder with hopping in all the three directions(periodic in x-direction) like the following figure. Please suggest me the way to generate such type of geometry. If possible then provide an example code for that for better understanding. [image: image.png] I will be very thankful to you. Naveen -- With Best Regards NAVEEN YADAV Ph.D Research Scholar Deptt. Of Physics & Astrophysics University Of Delhi.

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