Mailman 3 May 2018 - 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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LDOS map and density plot for a 3D system
by PRIYANKA May 27, 2018

May 27, 2018

Dear Sir, I was trying to plot 2D LDOS map for a 3D system. I am using kwant.plotter.map and kwant.plotter.plot for plotting density and LDOS. But there is an error message showing " Only 2D system can be plotted in this way". The following part is included where I am getting this error. Thanks in advance. def density(sys, energy, lead_nr, params=params): wf = kwant.wave_function(sys, energy, params=params) return (abs(wf(lead_nr))**2).sum(axis=0) d = density(sys,0.5, 0, params=params) print (d) kwant.plotter.map(sys, d, cmap='gist_heat_r', colorbar=True)#, site_lw=0) ldos = kwant.ldos(sys, energy=0.5, params=params) print (ldos) kwant.plotter.plot(sys, ldos, num_lead_cells=2) Regards, priyanka

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seeking help
by shyam lochan bora May 23, 2018

May 23, 2018

Dear Sir, I am a beginner user of kwant i want to make a ring shaped structure of bi2se3 .it is rhombohedral having lattice constants a = 4.138, c = 28.64. Internal coordinates u = 0.399 for Bi sites v= 0.206 for Se sites. The basic unit cell of Bi2Se3 is called Quituple layer which contains 5 atoms, one Se atom at (0,0,0), Bi atoms at internal coordinates(+_u,+_,u+_u) and Se atoms at (+-v,+-v,+-v) The Bravis lattice vectors are a1 = (-a/2,-a/2*sqrt(3),c/3) a2 = (a/2,-a/2*sqrt(3),c/3) a3=(0,-a/sqrt(3), c/3) for bi2Se3 i wrote the following program..Please tell whether it is correct or not and please tell how to form a ring structure of bi2se3 from math import pi, sqrt, tanh import kwant # For computing eigenvalues import scipy.sparse.linalg as sla # For plotting from matplotlib import pyplot # Define bismuth selenide lattice a= 4.138 c= 28.64 u= 0.399 v= 0.206 bismuthselenide = kwant.lattice.general([(-4.138/2,-4.138/2*sqrt(3),28.64/3),(4.138/2,-4.138/2*sqrt(3),28.64/3),(0,-4.138/sqrt(3),28.64/3)], [(0, 0, 0),(0.399, 0.399, 0.399),(0.206, 0.206, 0.206)]) a, b, c = bismuthselenide.sublattices

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Hamiltonian not hermician for an infinite wire with random complex hopping
by alexandre.bernard1＠u-psud.fr May 22, 2018

May 22, 2018

Hello (again), Everything is in the title. I want to implement random (and complex) next nearest neighbors hopping in a Haldane infinite wire. Without the random part, 'kwant.plotter.bands()' correctly plot the band structure of my system. However, when I add a random contribution on the modulus of the NNN hopping term, I get an error from 'kwant.plotter.bands()' : 'The cell Hamiltonian is not Hermitian' Which is strange because I red everywhere that the hermicity constraint is always fullfilled using Kwant. The function for random NNN hopping works perfectly fine for a finite system. So, is this comming from the inter-cell hopping terms ? If so, how to correct it ? Kwant does not consider the hopping terms of both ends of the cell as being equal ? It should be because u_k(r) = u_k(r+R) is like periodic boundary conditions for u_k. I add my script at the end so you can see for yourself (the NNN hopping randomness parameter is 'rand_nnn'). Best regards, Alexandre BERNARD ----------------- my script ---------------------- from types import SimpleNamespace import matplotlib import math from matplotlib import pyplot from mpl_toolkits import mplot3d import numpy as np import random import kwant def random_uni(param): return param*(random.random() - 0.5)*2 # returns a random number between +param and -param def onsite(site, p): # Here we affect a potential whose sign depends on which sublattice the atom lives in (breaking sublattice symmetry) if site.family == A: # sublattice A return p.m + random_uni(p.rand_os) else: # sublattice B return -p.m + random_uni(p.rand_os) def nn_hopping(site1, site2, params): return params.t_1 + random_uni(params.rand_nn) def nnn_hopping(site1, site2, params): return (math.cos(params.phi) + 1j*math.sin(params.phi)) * (params.t_2 + random_uni(params.rand_nnn)) def ribbon_shape_armchair(pos): return (-1 <= pos[0] < w) def hopping_color(site1, site2): if site1.family == A and site2.family == A: return 'b' elif site1.family == B and site2.family == B: return 'r' else: return '0.5' def site_color(site): if site.family == A: return 'b' else: return 'r' np.random.seed(271828) # Fixing the RNG seed for reproducibility (or not, because of how Kwant works) # Graphene lattice "pointing up", with two sublattices graphene = kwant.lattice.general([[1, 0], [1/2, np.sqrt(3)/2]], # Here are the vectors of the Bravais lattice [[0, 0], [0, 1/np.sqrt(3)]]) # Here are the positions of the atoms in the unit cell A, B = graphene.sublattices w = 29 # width of the ribbon p = SimpleNamespace(t_1=1.0, t_2=0.1, m=0.0, phi=np.pi/2, rand_os=0., rand_nn=0., rand_nnn=0.1) # Creation of the list of (oriented) bonds that will have the complex hopping term nnn_hoppings_A = (((-1, 0), A, A), ((0, 1), A, A), ((1, -1), A, A)) # Bonds within the A sublattice nnn_hoppings_B = (((1, 0), B, B), ((0, -1), B, B), ((-1, 1), B, B)) # Bonds within the B sublattice nnn_hoppings = nnn_hoppings_A + nnn_hoppings_B haldane_armchair = kwant.Builder(kwant.TranslationalSymmetry((0, 1*np.sqrt(3)))) haldane_armchair[graphene.shape(ribbon_shape_armchair, (0, 0))] = onsite haldane_armchair[graphene.neighbors(1)] = nn_hopping haldane_armchair[[kwant.builder.HoppingKind(*hopping) for hopping in nnn_hoppings]] = nnn_hopping kwant.plot(haldane_armchair, site_color=site_color, hop_color=hopping_color, fig_size=(6, 9)); kwant.plotter.bands(haldane_armchair.finalized(), args=[p], fig_size=(12, 8));

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seeking help
by shyam lochan bora May 18, 2018

May 18, 2018

Dear Sir, I want to model a bi2se3 nanowire in kwant to investigate the transport properties. Please help me in this regard. Regards, Shyam Lochan Bora Dept. of Physics. Dibrugarh University Assam, India

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Re: [Kwant] Installation error on Mac
by Bas Nijholt May 15, 2018

May 15, 2018

Hi Girish, Currently the recommended way to install kwant on macOS is with conda. See the instructions on https://kwant-project.org/install# Best, Bas > On 15 May 2018, at 09:20, Girish Sharma <girishs(a)g.clemson.edu> wrote: > > Dear All, > > I am trying to install Kwant on my Mac High Sierra 10.13.4. I am facing the following error after brew tap homebrew/science command: > > brew tap homebrew/science > Updating Homebrew... > ==> Auto-updated Homebrew! > Updated 1 tap (homebrew/core). > ==> Updated Formulae > aptly gtksourceview@4 nano rocksdb > armadillo jhiccup node-build solr > dash kubernetes-helm osquery spigot > dscanner libu2f-host pam-u2f spring-roo > fabric maxwell postgrest > fn mercurial pound > grpc mpc proguard > > Error: homebrew/science was deprecated. This tap is now empty as all its formulae were migrated. > > Could any one of you please help me with this. > > Thank you. > > Best regards, > Girish

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Installation error on Mac
by Girish Sharma May 15, 2018

May 15, 2018

Dear All, I am trying to install Kwant on my Mac High Sierra 10.13.4. I am facing the following error after brew tap homebrew/science command: brew tap homebrew/science Updating Homebrew... ==> *Auto-updated Homebrew!* Updated 1 tap (homebrew/core). ==> *Updated Formulae* aptly gtksourceview@4 nano rocksdb armadillo jhiccup node-build solr dash kubernetes-helm osquery spigot dscanner libu2f-host pam-u2f spring-roo fabric maxwell postgrest fn mercurial pound grpc mpc proguard *Error: homebrew/science was deprecated. This tap is now empty as all its formulae were migrated.* Could any one of you please help me with this. Thank you. Best regards, Girish

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