Mailman 3 July 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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Group velocites in the leads
by Luca Lepori Aug. 9, 2019

Aug. 9, 2019

Dear Kwant developers, I write concerning the group velocites of the modes in the leads. In particular, I wonder how Kwant calculates them. I see two possibilities (leads along x): 1) knowing the dispersion along x, from the usual definition v(kx) = \partial E(kx) / \partial kx; 2) working equivalently in the real space basis, and in particular on a unitary cell of a lead, one can calculate vx also as: vx = <\psi |i [H, \hat{x}] | \psi>, being \psi the wavefunction of the mode and H the Hamiltonian respectively, both defined on the unitary cell of the lead, and \hat{x} the position operator. The second approach can be useful also to estimate the expectation value of the velocities in the direction orthogonal to the leads (say when close boundary conditions are assumed). Does Kwant utilizes directly one of these two strategies ? Thank you very much and best regards L. L.

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Re: [Kwant] Periods for kwant.TranslationalSymmetry
by Barış Özgüler Aug. 5, 2019

Aug. 5, 2019

Hi Ousmane et al, I actually want the block of unit cells to be perpendicular to the scattering region as in the Wanted_System.png, attached. Note that it is a representative plot, I didn't produce it via Kwant but I want to attach the red lead to the black region in that direction, not like in Unwanted_System.png, which is also attached and produced via the code: ########################################## import kwant import numpy as np import matplotlib.pyplot as plt from types import SimpleNamespace def make_system(a, W, L): def shape(pos): (x, y) = pos return (0 <= y <= W/2 and -x/2 <= y <= (-x + L)/2) # or (-W <= y <= 0 and 0 <= x <= L) def onsite(site, par): return 4 * par.t - par.mu def hopx(par): return -par.t def hopy(par): return -par.t # lead lat = kwant.lattice.square(a, norbs=1) syst = kwant.Builder() syst[lat.shape(shape, (0, 0))] = onsite syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy lead = kwant.Builder(kwant.TranslationalSymmetry((-a, -2*a))) def lead_shape(pos): (x, y) = pos return -W <= x <= 0 def lead_hopx(site1, site2, par): return -par.t def lead_onsite(site, par): return 4 * par.t - par.mu lead[lat.shape(lead_shape, (-2*a, -a))] = lead_onsite lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = lead_hopx lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy syst.attach_lead(lead) syst = syst.finalized() return syst syst = make_system(a=5, W=100, L=100) kwant.plot(syst) ########################################## I couldn't make the lead rotated in the perpendicular direction to the surface. Is there a way to do it? Thanks, Barış

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Bound states calculation
by Oleksii Maistrenko July 17, 2019

July 17, 2019

Dear kwant researches, I came across the algorithm described in https://scipost.org/SciPostPhys.4.5.026, and I think I would benefit a lot from it. I am wondering whether it is implemented in the new kwant 1.4 library, or is there an implementation publicly available somewhere? Thanks, Oleksii

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Phlead.py
by Naveen Yadav July 16, 2019

July 16, 2019

Dear all, Could anyone provide me the newer version of code *phlead.py* to calculate the conductance through majorana. The older vesion of code is not working well with latest version of kwant and it shows a lot of errors. Please help me in this regard. Thank you. Best regards Naveen Naveen Department of Physics & Astrophysics University of Delhi New Delhi-110007

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Mobius Structure using Kwant
by Nuwan Chaminda Gunawardhana Waduge July 9, 2019

July 9, 2019

Dear all, I have a code for the Mobius structure, using python scripts. However, I want to construct a structure by adding hexagonal lattices in a Mobius structure. How can I do this using Kwant. Thank you in advance. Best, Nuwan, MSU, Starkville P.S.: The python script for the mobius structure is as follows: import numpy as np import matplotlib.pyplot as plt import matplotlib.tri as mtri from mpl_toolkits.mplot3d import Axes3D fig = plt.figure(figsize=plt.figaspect(0.5)) u = np.linspace(0, 2.0 * np.pi, endpoint=True, num=50) v = np.linspace(-0.5, 0.5, endpoint=True, num=10) u, v = np.meshgrid(u, v) u, v = u.flatten(), v.flatten() x = (1 + 0.5 * v * np.cos(u / 2.0)) * np.cos(u) y = (1 + 0.5 * v * np.cos(u / 2.0)) * np.sin(u) z = 0.5 * v * np.sin(u / 2.0) tri = mtri.Triangulation(u, v) ax = fig.add_subplot(1, 2, 1, projection='3d') ax.plot_trisurf(x, y, z, triangles=tri.triangles) ax.set_zlim(-1, 1) plt.show()

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Re: [Kwant] Periods for kwant.TranslationalSymmetry
by Barış Özgüler July 6, 2019

July 6, 2019

Hi Ousmane, How can I make sure that there is no overlap between the lead and normal region? Lead_shape() returns -L <= x <= L and we want the lead to satisfy x <= 0. If we don't use color_site(site), then we would get the attached plot. The black region not only represents the normal region but also represents the lead. However, the lead may also cover the region of x > 0 as the function Lead_shape() suggests. Is there another way to check what part of the shape is scattering region, what part is lead? Thanks, -- A. Barış Özgüler PhD Candidate in Physics https://home.physics.wisc.edu/ozguler/ University of Wisconsin–Madison Madison, Wisconsin 53706, USA

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