Kwant-discuss February 2018

kwant-discuss@python.org

5 participants
9 discussions

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>

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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))

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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

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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

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Conductance for a rectangular geometry
by amrita chapagain 24 Feb '18

24 Feb '18

Thank you Adel for prompt reply. I have another query here. Can I add these two system together incorporating missing hopping elements?

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Conductance for a rectangular geometry
by amrita chapagain 22 Feb '18

22 Feb '18

Hi, I want to add two leads on left instead. I have attached two leads and try to find conductance and compare with just one lead on left. The results for two leads and just one lead is not same. Can you help me what I am doing wrong here? I have attached my code here. import kwant # Recursive green function method import numpy as np # Module with advanced math commands from matplotlib import pyplot from numpy import sqrt from math import * #====================================================================== # Define the shape ------------------- #====================================================================== def wv_shape(pos): x, y = pos return (np.abs(2.0*x)<=L)&(np.abs(y)<W1/2.0) #---------------------------------------------------------------------- a = 1; # Lattice constant t = 1; # Coupling between sites E0L = 0*t # On-site potential in the lead L = 18; # Length of the W1 = 90; # Width on the left # Define geometry -------------------------------------------------------------------------- sys0 = kwant.Builder() lat = kwant.lattice.square(a) #-------------------------------------------------------------------------------------------- # Define onsite energies and couplings ---------------------------------------------------- sys0[lat.shape(wv_shape,(0,0))] = E0 # To make all sites the same sys0[lat.neighbors()] = t #-------------------------------------------------------------------------------------------- # Left lead ---------------------------------------------------------------------------------- left_lead1 = kwant.Builder(kwant.TranslationalSymmetry([-1,0])) # The lead goes to minus infinity left_lead2 = kwant.Builder(kwant.TranslationalSymmetry([-1,0])) # The lead goes to minus infinity left_lead1[(lat(0,y) for y in range(int(-W1/2+1),0))] = E0L left_lead2[(lat(0,y) for y in range(0,int(W1/2)))] = E0L left_lead1[lat.neighbors()] = t # Couplings in the lead left_lead2[lat.neighbors()] = t # Couplings in the lead sys0.attach_lead(left_lead1); sys0.attach_lead(left_lead2); #-------------------------------------------------------------------------------------------- # Right lead --------------------------------------------------------------------------------- right_lead = kwant.Builder(kwant.TranslationalSymmetry([1,0])) # The lead goes to plus infinity right_lead[(lat(0,y) for y in range(int(-W1/2+1),int(W1/2)))] = E0L right_lead[lat.neighbors()] = t # Couplings in the lead sys0.attach_lead(right_lead); #--------------------------------------------------------------------------------------------- sys = sys0.finalized() kwant.plot(sys); # Plots the shape def plot_conductance(sys, energies): data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) data.append(smatrix.transmission(2, 0)+smatrix.transmission(1,2) ) #transmission from left 2 leads to right lead pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() energies=[-3+i*0.02 for i in range(100)] plot_conductance(sys,energies)

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Hall mobility in a closed system
by elchatz＠auth.gr 20 Feb '18

20 Feb '18

Hello all, Is it posible to calculate the Hall mobility in a closed system using kwant? -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

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Saving a figure of the system
by elchatz＠auth.gr 17 Feb '18

17 Feb '18

Hello, I have just started using kwant, and I am trying to write a code excerpt that saves a figure of my system, but I just get a blank 3-D space. The code is the following, as taken by the TBModels website: ----------------------------------------------------------------- import kwant import tbmodels import wraparound import numpy as np import scipy.linalg as la import matplotlib matplotlib.use('agg') import matplotlib.pyplot as plt model = tbmodels.Model.from_wannier_files( hr_file='..._hr.dat', wsvec_file='..._wsvec.dat', xyz_file='..._centres.xyz', win_file='....win' ) lattice = model.to_kwant_lattice() wire = kwant.Builder() def shape(p): x, y, z = p return -20 < x < 20 and -5 < y < 5 and -5 < z < 5 wire[lattice.shape(shape, (0, 0, 0))] = 0 model.add_hoppings_kwant(wire) fig = plt.figure() ax = plt.subplot() ax = kwant.plot(wire) plt.savefig('wire.png') ---------------------------------------------------------------------------------------- If anyone knows whether the problem is with the system or with the plotting it would be greatly appreciated. Regards -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

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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()

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Kwant-discuss February 2018