Mailman 3 March 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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initial wave packet input
by 张金龙 April 22, 2019

April 22, 2019

Dear Colleagues: I have a question about Kwant realization: Can we input a initial wave packet and get the conductance or the final state? Could you give some suggestions? 3Q Best wishes!!! -- Jinlong Zhang jlzhang(a)163.com

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Re: [Kwant] Want to know more about bulid_discretized
by Bas Nijholt March 29, 2019

March 29, 2019

It seems like the documentation here <https://gitlab.kwant-project.org/kwant/kwant/blob/fdd4674/kwant/continuum/d…> is wrong because it expects a dictionary. I see that you do template = kwant.continuum.discretize_symbolic(hamiltonian) t = kwant.continuum.build_discretized(template, coords = ('x','y','z')) However, discretize_symbolic returns two variables. Instead do: template, coods = kwant.continuum.discretize_symbolic(hamiltonian) t = kwant.continuum.build_discretized(template, coords) The list of coods should be passed to discretize_symbolic. However, if you omit it, it will be inferred from your Hamiltonian’s k_{x, y, z} terms. Best, Bas On Fri, Mar 29, 2019 at 3:11 PM Naveen Yadav <naveengunwal72(a)gmail.com> wrote: > Hi Bas, > > Thanks for your reply. > > I have used the same syntax. But it is showing an Attribute Error: 'tuple > object has no attribute 'items' > > from __future__ import division > import kwant > import kwant.continuum > import scipy.sparse.linalg > import scipy.linalg > import numpy as np > import sympy > from math import sin, cos, sqrt, pi > import matplotlib.pyplot as plt > hamiltonian = ("""k_x**2 + k_y**2 + k_z**2""") > hamiltonian = kwant.continuum.sympify(hamiltonian) > template = kwant.continuum.discretize_symbolic(hamiltonian) > t = kwant.continuum.build_discretized(template, coords = ('x', 'y', 'z')) > print(t) > > AttributeError Traceback (most recent call last)<ipython-input-12-9780451ce368> in <module> 11 hamiltonian = kwant.continuum.sympify(hamiltonian) 12 template = kwant.continuum.discretize_symbolic(hamiltonian)---> 13 t = kwant.continuum.build_discretized(template, coords = ('x','y','z')) 14 print(t) 15 hamiltonian > /usr/local/lib/python3.6/dist-packages/kwant/continuum/discretizer.py in build_discretized(tb_hamiltonian, coords, grid_spacing, locals) 281 282 with reraise_warnings():--> 283 for k, v in tb_hamiltonian.items(): 284 tb_hamiltonian[k] = sympify(v, locals) 285 > AttributeError: 'tuple' object has no attribute 'items' > > What should I do. > > Naveen > > > On Fri, Mar 29, 2019 at 5:37 PM Bas Nijholt <basnijholt(a)gmail.com> wrote: > >> Hi Naveen, >> >> In the documentation >> <https://kwant-project.org/doc/dev/reference/generated/kwant.continuum.build…> >> you can see that coords require a sequence of strings, so for example: >> >> coords = ('x',) # for 1D >> coords = ('x', 'y', 'z') # for 3D >> >> Best, Bas >> >> On Fri, Mar 29, 2019 at 12:59 PM Naveen Yadav <naveengunwal72(a)gmail.com> >> wrote: >> >>> I want to know more about the builid_discretized(tb_hamiltonian, coords). >>> I did not undersand what should be the syntax to write the coords.Could >>> you please help me by sending an example code for writing coords? >>> >>> Thanks in Advance. >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> Naveen >>> Department of Physics & Astrophysics >>> University of Delhi >>> 110007 >>> >> > > -- > > > With Best Regards > NAVEEN YADAV > Ph.D Research Scholar > Deptt. Of Physics & Astrophysics > University Of Delhi. >

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Want to know more about bulid_discretized
by Naveen Yadav March 29, 2019

March 29, 2019

I want to know more about the builid_discretized(tb_hamiltonian, coords). I did not undersand what should be the syntax to write the coords.Could you please help me by sending an example code for writing coords? Thanks in Advance. Naveen Department of Physics & Astrophysics University of Delhi 110007

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Re: [Kwant] Problem with semimetals
by Luca Lepori March 22, 2019

March 22, 2019

Dear Joe, concerning to your answer https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg01808.html , I checked that I do not have any sign problem, as those you described, in my system/code. Therefore I am wandering if some fuzzy problem of matching of wavefunctions is known, or expected, to occur when metals (leads) and semimetals (scattering region) are put in contact (perhaps due to symmetries of whatever), not depending on the sign problem. I also attach below the code that I used, and that looks me correct, after various checks on the spectrum of the scattering region and of the leads. I assumed a cubic lattice with periodic boundary conditions along x and z, while the leads are along y. However, I checked that the problem persists also assuming open boundary conditions. Thank you very much for the help and best regards L. ----------------------------------------------------------------------------------- import kwant import math import cmath import scipy.sparse.linalg as sla import numpy # For plotting from matplotlib import pyplot # For matrix support import tinyarray #----------------------------------------------------- # We define Pauli-matrices 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]]) # We define the variables and the constants t = 1.0 v = 1.0 L = 13 # length y W = 13 # length x and z k0 = math.pi/10. #k0 = -0.4636476090008061 m0 = math.cos(k0) vtilde = v/math.sin(k0) h = vtilde*m0 + 2*v a=1 #--------------------------------------------------------------------------------------------------------- syst = kwant.Builder() lat = kwant.lattice.cubic(a) for i in range(W): for j in range(L): for k in range(W): # On-site Hamiltonian syst[lat(i, j, k)] = h*sigma_x # Hopping in x-direction if i > 0: syst[lat(i, j, k), lat(i - 1, j, k)] = -(vtilde/2)*sigma_x # Hopping in y-direction if j > 0: syst[lat(i, j, k), lat(i, j - 1, k)] = -(v/2)*((1j)*sigma_y + sigma_x) # Hopping in z-direction if k > 0: syst[lat(i, j, k), lat(i, j, k - 1)] = -(v/2)*((1j)*sigma_z + sigma_x) # I close hopping in x-direction, connecting W-1 and 0 for j in range(L): for k in range(W): syst[lat(0, j, k), lat(W-1, j, k)] = -(vtilde/2)*sigma_x # I close the hopping in z-direction, connecting W-1 and 0 for i in range(W): for j in range(L): syst[lat(i, j, 0), lat(i, j, W-1)] = -(v/2)*((1j)*sigma_z + sigma_x) #--------------------------------------------------------------------------------------------------------- # We define the right lead, along y sym_right_lead = kwant.TranslationalSymmetry((0, a, 0)) right_lead = kwant.Builder(sym_right_lead) for i in range(W): for k in range(W): right_lead[lat(i, 0, k)] = mu*sigma_0 if i > 0: right_lead[lat(i, 0, k), lat(i-1, 0, k)] = -t*sigma_0 if k > 0: right_lead[lat(i, 0, k), lat(i, 0, k-1)] = -t*sigma_0 right_lead[lat(i, 1, k), lat(i, 0, k)] = -t*sigma_0 # I close hopping in x-direction, connecting W-1 and 0 for k in range(W): right_lead[lat(0, 0, k), lat(W-1, 0, k)] = -t*sigma_0 # I close hopping in z-direction, connecting W-1 for i in range(W): right_lead[lat(i, 0, 0), lat(i, 0, W-1)] = -t*sigma_0 syst.attach_lead(right_lead) left_lead = right_lead.reversed() syst.attach_lead(left_lead)

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Updating Kwant paper and APS tutorials code
by WONG, Sheung Chuen March 21, 2019

March 21, 2019

Dear all, I am just a beginner on Kwant and downloaded Kwant 1.4. It is quite frustrated on getting syntax errors using full sample code from Kwan paper or APS tutorial which themselves provide very good introduction. For example, in Kwant paper Appendix D.5, smatrix = kwant.smatrix(sys, energy, args=[phi, ""]) doesn't work. Then I have modified to smatrix = kwant.smatrix(sys, energy,params=(phi=phi,salt="" ) it still doesn't work. Could anyone help? There are so many codes in Kwant paper and APS tutorial which relies on old version of Kwant. It would really be very helpful to keep the sample codes updated. Thanks a lot. Clement

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Dephasing effect
by 张金龙 March 19, 2019

March 19, 2019

Dear Sir. I have a question about Kwnat. Can we calculate the systems considered with the dephasing effects by Kwant? For example, just add a non-hermite terms in the onsite potential or add the non-hermite hopping between (i,j) and (j,i) leading the Hamiltonian no longer hermite ? -- Jinlong Zhang jlzhang(a)163.com

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