Mailman 3 October 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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Extract wavefunction for one lattice
by Yuhao Kang Nov. 2, 2018

Nov. 2, 2018

Hello, In the system I use two lattices to represent spin up and down. lat_u = kwant.lattice.honeycomb(a=1, name='up') lat_d = kwant.lattice.honeycomb(a=1, name='down') When I obtain the scattering wave functions from wf=kwant.wave_function(sys, en), it contains the value for both lat_u and lat_d. Is that possible to extract the wave function only for lat_u or lat_d? I tried to separate the wave function based on the odd/even index, but it is not the right sequence. Thank you in advance. Regards, Yuhao

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Re: [Kwant] Kwant-discuss Digest, Vol 62, Issue 13
by kuangyia lee Oct. 25, 2018

Oct. 25, 2018

Hi Leon, Thank your for the kind suggestion. But can you show me how to get download of your attached jupyter notebook. Thanks again ! Regards, Kuangyia On Wed, Oct 24, 2018 at 10:38 PM <kwant-discuss-request(a)kwant-project.org> wrote: > 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. plotting band structure of bulk 2D material along high > symmetry lines in the Brillouin zone (kuangyia lee) > 2. Re: plotting band structure of bulk 2D material along high > symmetry lines in the Brillouin zone (Maurer, Leon) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Wed, 24 Oct 2018 18:52:49 +0200 > From: kuangyia lee <kuangyia.lee(a)gmail.com> > To: kwant-discuss(a)kwant-project.org > Subject: [Kwant] plotting band structure of bulk 2D material along > high symmetry lines in the Brillouin zone > Message-ID: > <CAPVHYSmaFEHTHmKdh63u0RfWp+rJ15DP84bY== > gG-v+93W8ncA(a)mail.gmail.com> > Content-Type: text/plain; charset="utf-8" > > Dear kwant developers and users, > > I want to calculate and plot the band structure of bulk 2D material along > some high-symmetry lines in the Brillouin zone (e.g. Gamma-->K-->M--Gamma), > i.e. the 1D band structure. > > I found that someone already posted a relevant issue and some useful > solutions were also given. For example, see > > https://kwant-discuss.kwant-project.narkive.com/2fT27IJh/kwant-for-bulk-sys… > . > > > However, these solutions are only for calculating and plotting the full 2D > band structure in the Brillouin zone. > > Can anyone give some useful solutions to my concern? Your help is much > appreciated. > > Thank you and best regards, > Kuangyia Lee >

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plotting band structure of bulk 2D material along high symmetry lines in the Brillouin zone
by kuangyia lee Oct. 25, 2018

Oct. 25, 2018

Dear kwant developers and users, I want to calculate and plot the band structure of bulk 2D material along some high-symmetry lines in the Brillouin zone (e.g. Gamma-->K-->M--Gamma), i.e. the 1D band structure. I found that someone already posted a relevant issue and some useful solutions were also given. For example, see https://kwant-discuss.kwant-project.narkive.com/2fT27IJh/kwant-for-bulk-sys…. However, these solutions are only for calculating and plotting the full 2D band structure in the Brillouin zone. Can anyone give some useful solutions to my concern? Your help is much appreciated. Thank you and best regards, Kuangyia Lee

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Re: [Kwant] plotting band structure of bulk 2D material along high symmetry lines in the Brillouin zone
by Maurer, Leon Oct. 24, 2018

Oct. 24, 2018

Hi Kuangyia, If I understand your question correctly, I have done this by extracting a Hamiltonian from the wrapped system using hamiltonian_submatrix (with whatever wavevector you want as an argument) and finding the eigenvalues of that matrix. I’ve attached a jupyter notebook that uses kwant to calculate Si’s band structure along high-symmetry directions. In the notebook, cell 6 is the relevant one. That said, others may know a cleaner way to do this. That said, what is your ultimate goal? If it’s simply to compute band structures of a bulk material, then you can just write down the matrix without kwant and find its eigenvalues. (I’ve attached a second notebook that does that.) I don’t think that kwant simplifies the process. If you want to later want to do some transport simulation, then starting with kwant could prove useful. -Leon From: Kwant-discuss <kwant-discuss-bounces(a)kwant-project.org> on behalf of kuangyia lee <kuangyia.lee(a)gmail.com> Date: Wednesday, October 24, 2018 at 10:53 AM To: "kwant-discuss(a)kwant-project.org" <kwant-discuss(a)kwant-project.org> Subject: [EXTERNAL] [Kwant] plotting band structure of bulk 2D material along high symmetry lines in the Brillouin zone Dear kwant developers and users, I want to calculate and plot the band structure of bulk 2D material along some high-symmetry lines in the Brillouin zone (e.g. Gamma-->K-->M--Gamma), i.e. the 1D band structure. I found that someone already posted a relevant issue and some useful solutions were also given. For example, see https://kwant-discuss.kwant-project.narkive.com/2fT27IJh/kwant-for-bulk-sys…. However, these solutions are only for calculating and plotting the full 2D band structure in the Brillouin zone. Can anyone give some useful solutions to my concern? Your help is much appreciated. Thank you and best regards, Kuangyia Lee

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Units of density
by Marc Vila Oct. 22, 2018

Oct. 22, 2018

Dear Kwant developers, I've found in other threads in the mailing list that the units of current is for example (unit of charge)/(hbar/unit of energy) (https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg01100.html). Also, the local density of states has units of energy/volume (https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00169.html?). My question is, what is the units of the output of the density operator? Is it energy/volume as well? I ask this because intuitively I view it as the square of the wavefunction, but it gives me values larger than 1 for each site when there is only 1 mode involved (see attached picture) ?so it is not just the probability of findinge the electron at that site because this should be maximum 1. I have also noticed that the values I get in the colorbar depend on the value of my hopping (e.g. case of graphene), but overall I'm not so sure of the units. Thank you again for your help. Kind regards, Marc

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issues with Current calculation
by Sergey Slizovskiy Oct. 20, 2018

Oct. 20, 2018

Dear all, I am trying new Kwant 1.3 features on a very simple example of graphene monolayer, and, apart from a standard well-working code I add: for x in sys.sites(): x.family.norbs=1 for x in leadxp.sites(): x.family.norbs=1 for x in leadxm.sites(): x.family.norbs=1 (to avoid norbs not defined error) ... J_0 = kwant.operator.Current(sys) wf = kwant.solvers.default.wave_function(sys, energy=0.01, args=[phi,chempot,0]) psi=wf(1) current = J_0(psi) I get the following suspicious message: The size of the file /home/sergey/.local/lib/python3.6/site-packages/kwant/operator.cpython-36m-x86_64-linux-gnu.so is 2734 KB. Do you really want to load it? After answering yes, I get the error message, caused by current = J_0(psi) : "The debugged program raised the exception unhandled ValueError "vector is incorrect shape" File: /home/sergey/.local/lib/python3.6/site-packages/kwant/operator.cpython-36m-x86_64-linux-gnu.so, Line: 529 Break here?" Could anyone guess, what goes wrong? N.B. I have installed Kwant with a command pip3 install kwant Thanks, Sergey

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