Mailman 3 January 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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Dangling bonds
by Sergio Castillo Robles Feb. 14, 2019

Feb. 14, 2019

Hello everyone, I would appreciate any suggestion you could give me to solve this: Im currently working on a 2D finite monolayer of certain material that is coupled to a pair of leads in both left and right sides, the thing is: how can I get rid of the dangling bonds that appears in the edges of the nanoribbon?, I cant use the function "eradicate dangling" because the dissapearing atoms will just generate new dangling bonds. (By the way: I tried to use this function just to see what happens but nothing changed in the structure, is that normal?) So, Is there a way to automatically fill the dangling bonds with Hydrogen atoms? Or do I have to do it manually? Thanks in advance.

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Using MUMPS to solve a large set set of linear equations
by sazeh_9999＠yahoo.com Jan. 26, 2019

Jan. 26, 2019

Dear Kwant developers, I created a general lattice with 10 million orbitals in Kwant and I obtained the Hamiltonian(H). At some point, I need to solve the inhomogeneous matrix equation H u = v, where u is the vector of unknowns and v is a constant vector. My life will be easier if I could use MUMPS solver provided by Kwant to obtain u. Is there any chance? Best regards,Hadi

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Ynt: Ynt: Re: Ynt: Re: Datta’s ballistic transport formalism vs KWANT
by mutcran Jan. 23, 2019

Jan. 23, 2019

Thanks Adel, I realized that I used round function instead of floor and that caused the difference. Best, Ran � � � � Dear Adel, � Thank you for the additional remark. Yes, for near zero energies this "arcos formula" gives the same with Datta's simple expression. However, since you said it is exact for KWANT's discrete model, I tried to compare it with KWANT's results and I found discrepancy. Please see the attached figure. � In the Figure, you will see that I reduced "a" from 1 to 0.1 and KWANT results (blue curve) and it gave much closer to Datta's expression (yellow curve) now, as Joe predicted in the previous message. However, this "arcos expression" (green curve) does not give the same results with KWANT. And the results do not change much when decrease the lattice parameter a much lower like 0.00001. Am I doing sth wrong here or did I misinterpret your point? � Best, Ran � � Dear Mutcran, � I would like just to make an additional remark. Indeed, the formula in Datta's book is for a continuous model where the maximum number of modes is given by� M=2 W/ \lambda_f�� (\lambda_f is the Fermi wavelength). � In the case of a discrete model, like in Kwant, you can deduce M from the band structure. In fact, we have: E=4t -2t cos(kx)-2t cos(m pi/(N+1)), where N is the number of sites for one transversal cell. The maximum number of transmitted modes is obtained when the longitudinal kinetic energy is 0 (kx~0). so we get M= (N+1)/pi�� arcos((E-2t)/(-2t))�� (you need to take the integer part of this expression). This result is exact for a discrete square lattice model. A simple Taylor expansion around E~0 will give you the Datta's formula�� (where W=(N+1)a). � As a conclusion, the number of transmitted modes for a given discrete model is obtained from the form of the Band structure. This allows you to calculate it for any complex lattice (as long as you can get analytically the band structure). � I hope this helps, Adel � � � � On Tue, Jan 22, 2019 at 11:22 PM mutcran <mutcran(a)mynet.com> wrote: Thanks Joe! That was indeed the case! It became much closer with small a. Best, Ran � Hi Ran, > I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as > > Ttot=T(E)M(E) > > Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression? > Nice question! Looking at your results it seems that the energies at which new modes ope n is shifted with respect to Datta's result. I believe that this is simply due to the fact that your discretization is not fine enough. Datta's result is valid in the continuum limit, whereas the Kwant simulation (in the case presented) uses a finite-difference discretization to render the problem discrete. If you decrease the 'a' parameter, you should see the discrepancy between the two result decrease. Happy Kwanting, Joe -- Abbout Adel

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Ynt: Re: Ynt: Re: Datta’s ballistic transport formalism vs KWANT
by mutcran Jan. 23, 2019

Jan. 23, 2019

Dear Adel, � Thank you for the additional remark. Yes, for near zero energies this "arcos formula" gives the same with Datta's simple expression. However, since you said it is exact for KWANT's discrete model, I tried to compare it with KWANT's results and I found discrepancy. Please see the attached figure. � In the Figure, you will see that I reduced "a" from 1 to 0.1 and KWANT results (blue curve) and it gave much closer to Datta's expression (yellow curve) now, as Joe predicted in the previous message. However, this "arcos expression" (green curve) does not give the same results with KWANT. And the results do not change much when decrease the lattice parameter a much lower like 0.00001. Am I doing sth wrong here or did I misinterpret your point? � Best, Ran � � Dear Mutcran, � I would like just to make an additional remark. Indeed, the formula in Datta's book is for a continuous model where the maximum number of modes is given by� M=2 W/ \lambda_f�� (\lambda_f is the Fermi wavelength). � In the case of a discrete model, like in Kwant, you can deduce M from the band structure. In fact, we have: E=4t -2t cos(kx)-2t cos(m pi/(N+1)), where N is the number of sites for one transversal cell. The maximum number of transmitted modes is obtained when the longitudinal kinetic energy is 0 (kx~0). so we get M= (N+1)/pi�� arcos((E-2t)/(-2t))�� (you need to take the integer part of this expression). This result is exact for a discrete square lattice model. A simple Taylor expansion around E~0 will give you the Datta's formula�� (where W=(N+1)a). � As a conclusion, the number of transmitted modes for a given discrete model is obtained from the form of the Band structure. This allows you to calculate it for any complex lattice (as long as you can get analytically the band structure). � I hope this helps, Adel � � � � On Tue, Jan 22, 2019 at 11:22 PM mutcran <mutcran(a)mynet.com> wrote: Thanks Joe! That was indeed the case! It became much closer with small a. Best, Ran � Hi Ran, > I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as > > Ttot=T(E)M(E) > > Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression? > Nice question! Looking at your results it seems that the energies at which new modes open is shifted with respect to Datta's result. I believe that this is simply due to the fact that your discretization is not fine enough. Datta's result is valid in the continuum limit, whereas the Kwant simulation (in the case presented) uses a finite-difference discretization to render the problem discrete. If you decrease the 'a' parameter, you should see the discrepancy between the two result decrease. Happy Kwanting, Joe -- Abbout Adel

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attach-lead
by 张金龙 Jan. 23, 2019

Jan. 23, 2019

Dear Colleagues, I want to build a structure as shown in picture. There are 5 parts. I want to construct it by define the shape function shown in TUTORIAL: Nontrivial shapes. However, when I want to attach a 1D lead on the two-side, I get a message: ValueError: Sites with site families (kwant.lattice.Monatomic([[1.0, 0.0], [0.0, 1.0]], [0.0, 0.0], '', 4),) do not appear in the system, hence the system does not interrupt the lead. Can you give me some hints? Maybe my description is not clear, I attach the code in the e-mail to reproduce this question. Best wishes. Jinlong Zhang jlzhang1996(a)163.com

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Ynt: Re: Datta’s ballistic transport formalism vs KWANT
by mutcran Jan. 23, 2019

Jan. 23, 2019

Thanks Joe! That was indeed the case! It became much closer with small a. Best, Ran � Hi Ran, > I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as > > Ttot=T(E)M(E) > > Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression? > Nice question! Looking at your results it seems that the energies at which new modes open is shifted with respect to Datta's result. I believe that this is simply due to the fact that your discretization is not fine enough. Datta's result is valid in the continuum limit, whereas the Kwant simulation (in the case presented) uses a finite-difference discretization to render the problem discrete. If you decrease the 'a' parameter, you should see the discrepancy between the two result decrease. Happy Kwanting, Joe

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