Kwant-discuss September 2019

kwant-discuss@python.org

10 participants
13 discussions

Gate-defined Nanowire Quantum Dot
by Jonathan Fields 15 Sep '22

15 Sep '22

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 06 Mar '22

06 Mar '22

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 06 Mar '22

06 Mar '22

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 12 Sep '21

12 Sep '21

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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Hopping for random sites
by Ali Asgharpour 02 Oct '19

02 Oct '19

Hello, Would you please let me know how I can add nn and nnn hoppings for random sites (not all) in graphene? Best regards, Ali

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Kwant scattering wave function vs Green's function comparison
by Amrit Poudel 18 Sep '19

18 Sep '19

Hello Kwant users, I am trying to compare the retarded Green's function of a simple 1D wire attached to two leads using two different methods: (I) Using scattering wave function obtained from the Kwant software and using Eq. 25 in energy domain of "Numerical simulations of time resolved quantum electronics (https://arxiv.org/abs/1307.6419) written by Kwant authors. (II) Direct computation of the retarded Green's function by inverting device Hamiltonian with self energies of the attached leads (again computed from the Kwant software): G^r(E) = [E+\i*\eta - H- \Sigma^r_{leads}]^{-1} for a relatively small system size (5 sites in the attached example). Here both H and \Sigma^r are computed from the Kwant software. However, I find that these two results do not agree even in a simple 1D example when on-site potential is present in the few sites of device or scattering region only. I have attached the Python script with this email. Does anyone know the reason behind the discrepancy between the two methods?I would greatly appreciate any comments/suggestions on how we can resolve this error? Thanks!

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Plotting energy as a function of magnetic field in 3D.
by Naveen Yadav 13 Sep '19

13 Sep '19

Dear Sir, I am trying to plot the energy as a function of magnetic field for a 3D case, but I am getting tedious results. The system is infinite in two directions and has some width in the third direction. Please have a look at the code attached below. I tried a lot but failed. Is the code correct or I am wrong somewhere. Thank you. *import kwantimport scipy.sparse.linalg as slaimport matplotlib.pyplot as pltimport tinyarrayimport numpy as npfrom numpy import cos, sin, piimport cmathfrom cmath import expsigma_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]])def make_system(a=1, L=30, W=10, H=10, t=1.0, t_x=1.0, t_y=1.0, t_z=1.0, lamda=0.1, beta=1.05): def onsite(site): return (t_z * cos(beta) + 2 * t) * sigma_z def hoppingx(site0, site1): return (-0.5 * t * sigma_z - 0.5 * 1j * t_x * sigma_x) def hoppingy(site0, site1): return -0.5 * t * sigma_z - 0.5 * 1j * t_y * sigma_y def hoppingz(site0, site1, B): y = site1.pos[1] return (-0.5 * t_z * sigma_z - 0.5 * 1j * lamda * sigma_0) * exp(2 * pi * 1j * B * a * (y-40)) syst = kwant.Builder() lat = kwant.lattice.cubic(a) syst[(lat(z, y, x) for z in range(H) for y in range(W) for x in range(L))] = onsite syst[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz syst[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy syst[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx lead1=kwant.Builder(kwant.TranslationalSymmetry((0,-a,0))) lead1[(lat(z,y,x) for z in range(H)for y in range(W)for x in range(L))]=onsite lead1[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz lead1[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy lead1[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx syst.attach_lead(lead1) syst.attach_lead(lead1.reversed()) lead2=kwant.Builder(kwant.TranslationalSymmetry((-a,0,0))) lead2[(lat(z,y,x) for z in range(H)for y in range(W)for x in range(L))]=onsite lead2[kwant.builder.HoppingKind((1, 0, 0), lat, lat)] = hoppingz lead2[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] = hoppingy lead2[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] = hoppingx syst.attach_lead(lead2) syst.attach_lead(lead2.reversed()) syst = syst.finalized() return systdef analyze_system(): syst = make_system() kwant.plot(syst) Bfields = np.linspace(0, 0.002, 100) energies = [] for B in Bfields: ham_mat = syst.hamiltonian_submatrix(params=dict(B=B), sparse=True) ev, evec = sla.eigsh(ham_mat.tocsc(), k=20, sigma=0) energies.append(ev) #print(energies) plt.figure() plt.plot(Bfields, energies) plt.xlabel("magnetic field [${10^-3 h/e}$]") plt.ylabel("energy [t]") plt.ylim(0, 0.11) plt.showdef main(): syst = make_system() analyze_system()main()* -- With Best Regards NAVEEN YADAV Ph.D Research Scholar Deptt. Of Physics & Astrophysics University Of Delhi.

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Difference between hop[0].tag and hop[1].tag
by Adel Belayadi 10 Sep '19

10 Sep '19

Dear users, Good day. My query is about hoppings. In fact, sometimes we have to change the onsite parameters when for instance a magnetic field is applied. What is the difference between hop[0].tag and hop[1].tag My second question the onsite fuction for example: def onsite(site, V):return V why it depends on site where the shape functions for example def circle(pos): rsq = pos[0] ** 2 + pos[1] ** 2 depends on pos Best A BELAYADI

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help conda
by 白春旭 10 Sep '19

10 Sep '19

Dear Sir, I have a problem to install Kwant when download the Pre-built packages ( Anaconda package ). That is to say I can't download the package. My operating systems is Microsoft Windows. Can you help me. Best regards, Chunxu Bai

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Re: [Kwant] How to solve the Hamiltonian matrix with off-diagonal terms?
by Joseph Weston 10 Sep '19

10 Sep '19

Hi, > We consider the values of the conservation law based on the > off-diagonal term of Hamiltonian matrix, details are as follows: > > > > H = tinyarray.array([[0, 0, 0, 1, 0, 0], > > [0, 0, 0, 0, 1, 0], > > [0, 0, 0, 0, 0, 1], > > [1, 0, 0, 0, 0, 0], > > [0, 1, 0, 0, 0, 0], > > [0, 0, 1, 0, 0, 0]]) > I don't really understand; is this the full Hamiltonian? > spin_block = tinyarray.array([[0, 0, 0, 1, 0, 0], > > [0, 0, 0, 0, 1, 0], > > [0, 0, 0, 0, 0, 1], > > [-1, 0, 0, 0, 0, 0], > > [0, -1, 0, 0, 0, 0], > > [0, 0, -1, 0, 0, 0]]) > > And we add “conservation_law= - spin_block” in “lead=kwant.Builder()” > > > > The program can not work, and prompt error: > > > > IndexError: index 2 is out of bounds for axis 0 with size 2 > There is not enough information for me to be able to help you. Please attach a complete Kwant script. Happy Kwanting, Joe

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Kwant-discuss September 2019