Mailman 3 June 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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Periods for kwant.TranslationalSymmetry
by Barış Özgüler June 30, 2019

June 30, 2019

Hi all, I want to attach a lead on a vertical surface. I have a problem with the periods for kwant.TranslationalSymmetry. When I choose (b = 2, c = 1) in the code below, I get the system plot. But the choice of (b = 1, c = 1) doesn't work. I want the period to be (b = 1, c = 1). Can someone help me understand why it doesn't work? ++++++++++++++++++++++++++++++++++++++++ import kwant import matplotlib.pyplot as plt def make_system(a, W, L): def shape(pos): (x, y) = pos return (-L <= x <= 0 and -L <= y <= L) def onsite(site, par): return 4 * par.t - par.mu def hopx(site1, site2, par): return -par.t def hopy(site1, site2, par): return -par.t 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 # (b = 2, c = 1) works, (b = 1, c = 1) does not work b = 1 c = 1 lead = kwant.Builder(kwant.TranslationalSymmetry((b*a, c*a))) #, time_reversal=1) def lead_shape(pos): (x, y) = pos return - L/2 <= y <= L/2 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, (0, 0))] = 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 a = 5 number_of_sites = 20 L=number_of_sites*a number_of_sites2 = 50 L2=number_of_sites2*a syst = make_system(a=a, W=L2, L=L) kwant.plot(syst); ++++++++++++++++++++++++++++++++++++++++ Thanks, Barış

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The unit of current of kwant.operator.Current
by Zang, Hang June 30, 2019

June 30, 2019

Dear Kwant users, I just have a question for the unit of the Kwant output current, I think there are 2 ways to calculate the current value: 1. By integrating the conductance data: for specific, for the conductance generated the code below: ==================================================== for ie in range(-50,50): energy = ie * 0.01 smatrix = kwant.smatrix(syst, energy) energies.append(energy) data.append(smatrix.transmission(1,0)) ==================================================== according to the manul, the energy of smatrix.transmission(1,0) is e^2/h, and since I buildup the system with the Hamiltonian with the unit of "hartree" I think the energy that I give to kwant.smatrix(syst,energy) is also hartree. I think if I want to get the current, according to eq.10 of the Kwant paper, I should change the "conductance-energy" data to "conductance-voltage" data and then directly integrate it. 2. By using kwant.operator.Current with the script below: ==================================================== wf = kwant.wave_function(syst,energy=-0.25) J = kwant.operator.Current(syst,where=[(syst.sites[0],syst.sites[1]),(syst.sites[1],syst.sites[2])],sum=True) current = sum(J(p) for p in wf(0)) ==================================================== I'm trying to calculate the total current at a certain "bias energy" (-0.25 hartree, since I build the system with Hamiltonian in unit of hartree) but I'm not quite clear with the unit of the output current. Besides, is the current calculated by the second method should be equal to the first method? Thanks in advance for your help. Hang Zang

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Re: [Kwant] Current and hopping index relationship
by Abbout Adel June 30, 2019

June 30, 2019

Dear Zang, 1) Your question concerning the calculation of the current for all the hoppings: That is exactly what you get when you do not specify the argument '' where" when you define the current. ie: J = kwant.operator.Current(syst) returns the current for all the hoppings. Do you know that you can get all the hoppings in the system by doing list(sys.hoppings()) with sys the non finalized system? 2) Yes you can calculate the current in the presence of a bias, but for that you need to do an integration over the contributions at all the energies with a weight of Fermi Dirac for each lead. but I don't see a bias in your example. I hope this helps, Adel On Sun, Jun 30, 2019 at 7:15 AM Zang, Hang <zanghang(a)email.gwu.edu> wrote Dear Adel and all Kwant users, Below is my script for calculating the current density based on the previous discussions (the main part might be the lines after "syst = syst.finalized()"), I just want to know is it correct to get the current density (for all the hoppings) and the corresponding h for a system at a certain bias? Thank you very much for your help. ################################################################################### import kwant primitive_vectors = [ (2.3,0.0) , (0.0,2.3) ] atomic_sites = [ (2.0,2.0), (1.0,1.0) , (0.0,0.0) , (-1.0,-1.0),(-2.0,-2.0), (1.0,0.0)] lat = kwant.lattice.Polyatomic(primitive_vectors , atomic_sites , norbs = 1) atoms = lat.sublattices #============================================================= syst = kwant.Builder() syst[atoms[0](0,0)] = 1 syst[atoms[1](0,0)] = 1 syst[atoms[2](0,0)] = 1 syst[atoms[3](0,0)] = 1 syst[atoms[4](0,0)] = 1 syst[atoms[5](0,0)] = 1 syst[atoms[0](0,0),atoms[1](0,0)] = -1 syst[atoms[1](0,0),atoms[2](0,0)] = -1 syst[atoms[2](0,0),atoms[3](0,0)] = -1 syst[atoms[3](0,0),atoms[4](0,0)] = -1 syst[atoms[2](0,0),atoms[5](0,0)] = -1 syst[atoms[1](0,0),atoms[5](0,0)] = -1 #============================================================ sym_up_lead = kwant.TranslationalSymmetry((0.0,2.3)) up_lead = kwant.Builder(sym_up_lead) up_lead[atoms[0](0,1)] = 1 up_lead[atoms[0](0,1),atoms[0](0,2)] = -2 syst.attach_lead(up_lead) #============================================================ sym_bottom_lead = kwant.TranslationalSymmetry((0.0,-2.3)) bottom_lead = kwant.Builder(sym_bottom_lead) bottom_lead[atoms[4](0,-1)] = 1 bottom_lead[atoms[4](0,-1),atoms[4](0,-2)] = -2 syst.attach_lead(bottom_lead) #============================================================ syst = syst.finalized() #=========================================================== tmp1 = kwant.plotter.sys_leads_sites(syst,num_lead_cells=0) tmp2 = kwant.plotter.sys_leads_pos(syst,site_lead_nr=tmp1[0]) tmp3 = kwant.plotter.sys_leads_hoppings(syst,num_lead_cells=0) tmp4 = kwant.plotter.sys_leads_hopping_pos(syst,hop_lead_nr=tmp3[0]) hopping_number = len(tmp3[0]) print(hopping_number) wf = kwant.wave_function(syst, energy=-1) J = kwant.operator.Current(syst,where=[(syst.sites[tmp3[0][i][0][0]],syst.sites[tmp3[0][i][0][1]]) for i in range(hopping_number)]) total_J=sum(J(p) for p in wf(0)) print(total_J) for i in range(hopping_number): print(tmp4[0][i],tmp4[1][i],total_J[i]) ################################################################################### Hang Zang > > On Sun, Jun 23, 2019 at 8:22 AM Abbout Adel <abbout.adel(a)gmail.com> wrote: > >> Dear Zang, >> >> If you do not specify the region where you want to calculate the current, >> kwant will do that for all the hoppings in your system. In your case, I >> guess that your system has 6 links (and thus 12 hoppings if we count the >> two directions). >> >> Please check the documentation concerning the argument "where": >> >> *where* : sequence of pairs of *int* or Site >> <https://kwant-project.org/doc/1/reference/generated/kwant.builder.Site.html…>, >> or callable, optional >> >> Where to evaluate the operator. If syst is not a finalized Builder, then >> this should be a sequence of pairs of integers. If a function is provided, >> it should take a pair of integers or a pair of Site >> <https://kwant-project.org/doc/1/reference/generated/kwant.builder.Site.html…> >> (if syst is a finalized builder) and return True or False. If not >> provided, the operator will be calculated over all hoppings in the system. >> >> >> >> >> If you want to calculate the current just for a given hopping you can do >> that as follows >> site1=lat(0,1) >> site1=lat(0,2) >> J(syst, where=[(site1,site2)]) >> If you want the current at a given set of hoppings, you just use >> where=[(site1,site2),(site3,site4),(site5,site6)....................] >> >> >> >> 2) The current that you get with kwant is actually the contribution of >> the wave function psi (or the mode p) at a given energy to the total >> current. >> Depending on what you want to get, you may need to sum over all the modes >> if you want to get the total current at the *Fermi surface* and >> Integrate over the whole band with Fermi Dirac distribution, if you want to >> get the total current of the *Fermi sea.* >> >> I hope this helps, >> Adel >> >> >> . >> >> >> >> On Fri, Jun 21, 2019 at 7:32 AM Zang, Hang <zanghang(a)email.gwu.edu> >> wrote: >> >>> Dear All, >>> >>> I'm trying to calculate the site-to-site current with kwant, >>> for a specific system, the output of >>> "kwant.plotter.sys_leads_hopping_pos" is like below: >>> (array([[-1., -1.], >>> [-1., -1.], >>> [ 0., 0.], >>> [ 0., 0.], >>> [ 1., 0.], >>> [ 1., 1.]]), array([[ 0., 0.], >>> [-2., -2.], >>> [ 1., 1.], >>> [ 1., 0.], >>> [ 1., 1.], >>> [ 2., 2.]])) >>> >>> For the current calculation of the same system, I use the command below: >>> ------------------------------------------------------------------ >>> wf = kwant.wave_function(syst, energy=-1) >>> psi = wf(0)[0] >>> J_0 = kwant.operator.Current(syst) >>> current = J_0(psi) >>> ------------------------------------------------------------------ >>> and the out put of "current" is like below: >>> [ 0.33230769 -0.33230769 0.33230769 0.22153846 -0.33230769 0.11076923 >>> -0.11076923 0.11076923 0.33230769 -0.22153846 -0.11076923 -0.33230769] >>> >>> I'm not clear about the exact correspondance between the element of >>> current (12 element) and the element of hopping (2 array), >>> could you plese give me some explanations about this? >>> >>> Also, I'm not sure that if I want to calculate the current at a certain >>> energy (like "-1" above), >>> do I have to calculate the current at all the wavefunction (like for all >>> p of wf(0)[p]) >>> or I have to calculate the current only at the wavefunction with >>> "negivate velocity"? >>> >>> Thanks in advance for your help. >>> Hang Zang >>> >> >> >> -- >> Abbout Adel >> > -- Abbout Adel

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Re: [Kwant] Kwant-discuss Digest, Vol 70, Issue 21
by Ousmane Ly June 29, 2019

June 29, 2019

Dear Suman, for plotting the system you just need to consider the function you defined for making it, not the empty Builder object use kwant.plot(make_cuboid()) instead of kwant.plot(syst). For attaching leads you need to define the corresponding shape as you did for the system and specify the translationally invariant direction (see kwant documentation for more details). Regards, Ousmane Le sam. 29 juin 2019 à 17:25, <kwant-discuss-request(a)kwant-project.org> a écrit : > Send Kwant-discuss mailing list submissions to > kwant-discuss(a)kwant-project.org > > To subscribe or unsubscribe via the World Wide Web, visit > https://mailman-mail5.webfaction.com/listinfo/kwant-discuss > or, via email, send a message with subject or body 'help' to > kwant-discuss-request(a)kwant-project.org > > You can reach the person managing the list at > kwant-discuss-owner(a)kwant-project.org > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Kwant-discuss digest..." > > > Today's Topics: > > 1. Fwd: Supercell building in Kwant (Suman Chowdhury) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sat, 29 Jun 2019 12:16:16 +0530 > From: Suman Chowdhury <sumanchowdhury88(a)gmail.com> > To: kwant-discuss(a)kwant-project.org > Subject: [Kwant] Fwd: Supercell building in Kwant > Message-ID: > <CABFgFhF2xqCzaC7O7qbXn0nVe=BcPTtb4ZJ_Scr= > r+g9zQ6yEQ(a)mail.gmail.com> > Content-Type: text/plain; charset="utf-8" > > Dear Kwant user, > I am trying to buil an extended system (supercell) by only defining its > lattice vectors and its unit cell coordinate. After doing that whenever I > am trying to plot the system, I am getting the following error : > > Traceback (most recent call last): > File "practice.py", line 49, in <module> > kwant.plot(syst) > File "/usr/lib/python3/dist-packages/kwant/plotter.py", line 834, in plot > sites_pos = sys_leads_pos(syst, sites) > File "/usr/lib/python3/dist-packages/kwant/plotter.py", line 475, in > sys_leads_pos > num_lead_cells = site_lead_nr[-1][2] + 1 > IndexError: list index out of range > ______________________________________________________________ > > Nothing has been mentioned in the Kwant manual. I am also pasting the > python code which I am trying to run : > > import kwant > import matplotlib.pyplot > from math import sqrt > > syst = kwant.Builder() > > # Defining the lattice > sin_45 = 1 / sqrt(2) > cos_45 = 1 / sqrt(2) > > lv=1 > > lat=kwant.lattice.general([(0,1),(1,0)],[(cos_45/2,sin_45/2),(cos_45/2+1,sin_45/2),(cos_45/2+1,-sin_45/2),(cos_45/2,-sin_45/2)]) > > a, b, c, d = lat.sublattices > > t = 1.0 > W=10 > L=10 > > syst = kwant.Builder() > > def make_cuboid(W=10, L=10): > def cuboid_shape(pos): > x, y = pos > return 0 <= x < W and 0 <= y < L > syst = kwant.Builder() > syst[lat.shape(cuboid_shape, (0, 0))] = None > syst[lat.a.neighbors()] = -0.5 > syst[lat.b.neighbors()] = 0.5 > syst[lat.c.neighbors()] = -0.5 > syst[lat.d.neighbors()] = 0.5 > return syst > > kwant.plot(syst) > > > I am requesting you to help me in this regard. Also please let me know how > should I attach leads according to my choice in the above system. > -- > *Dr. Suman Chowdhury* > > > > *Assistant Professor Dept. of Physics, Bangabasi College Kolkata- 700009, > West Bengal, India.* > * Ph no-+91-9830512232* >

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Fwd: Supercell building in Kwant
by Suman Chowdhury June 29, 2019

June 29, 2019

Dear Kwant user, I am trying to buil an extended system (supercell) by only defining its lattice vectors and its unit cell coordinate. After doing that whenever I am trying to plot the system, I am getting the following error : Traceback (most recent call last): File "practice.py", line 49, in <module> kwant.plot(syst) File "/usr/lib/python3/dist-packages/kwant/plotter.py", line 834, in plot sites_pos = sys_leads_pos(syst, sites) File "/usr/lib/python3/dist-packages/kwant/plotter.py", line 475, in sys_leads_pos num_lead_cells = site_lead_nr[-1][2] + 1 IndexError: list index out of range ______________________________________________________________ Nothing has been mentioned in the Kwant manual. I am also pasting the python code which I am trying to run : import kwant import matplotlib.pyplot from math import sqrt syst = kwant.Builder() # Defining the lattice sin_45 = 1 / sqrt(2) cos_45 = 1 / sqrt(2) lv=1 lat=kwant.lattice.general([(0,1),(1,0)],[(cos_45/2,sin_45/2),(cos_45/2+1,sin_45/2),(cos_45/2+1,-sin_45/2),(cos_45/2,-sin_45/2)]) a, b, c, d = lat.sublattices t = 1.0 W=10 L=10 syst = kwant.Builder() def make_cuboid(W=10, L=10): def cuboid_shape(pos): x, y = pos return 0 <= x < W and 0 <= y < L syst = kwant.Builder() syst[lat.shape(cuboid_shape, (0, 0))] = None syst[lat.a.neighbors()] = -0.5 syst[lat.b.neighbors()] = 0.5 syst[lat.c.neighbors()] = -0.5 syst[lat.d.neighbors()] = 0.5 return syst kwant.plot(syst) I am requesting you to help me in this regard. Also please let me know how should I attach leads according to my choice in the above system. -- *Dr. Suman Chowdhury* *Assistant Professor Dept. of Physics, Bangabasi College Kolkata- 700009, West Bengal, India.* * Ph no-+91-9830512232*

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Current and hopping index relationship
by Zang, Hang June 23, 2019

June 23, 2019

Dear All, I'm trying to calculate the site-to-site current with kwant, for a specific system, the output of "kwant.plotter.sys_leads_hopping_pos" is like below: (array([[-1., -1.], [-1., -1.], [ 0., 0.], [ 0., 0.], [ 1., 0.], [ 1., 1.]]), array([[ 0., 0.], [-2., -2.], [ 1., 1.], [ 1., 0.], [ 1., 1.], [ 2., 2.]])) For the current calculation of the same system, I use the command below: ------------------------------------------------------------------ wf = kwant.wave_function(syst, energy=-1) psi = wf(0)[0] J_0 = kwant.operator.Current(syst) current = J_0(psi) ------------------------------------------------------------------ and the out put of "current" is like below: [ 0.33230769 -0.33230769 0.33230769 0.22153846 -0.33230769 0.11076923 -0.11076923 0.11076923 0.33230769 -0.22153846 -0.11076923 -0.33230769] I'm not clear about the exact correspondance between the element of current (12 element) and the element of hopping (2 array), could you plese give me some explanations about this? Also, I'm not sure that if I want to calculate the current at a certain energy (like "-1" above), do I have to calculate the current at all the wavefunction (like for all p of wf(0)[p]) or I have to calculate the current only at the wavefunction with "negivate velocity"? Thanks in advance for your help. Hang Zang

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