Mailman 3 June 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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Onsite and hopping values in QHE
by elchatz＠auth.gr Sept. 15, 2018

Sept. 15, 2018

Hello everyone, I am trying to reproduce the QHE bar device calculations http://nbviewer.jupyter.org/github/topocm/topocm_content/blob/master/w3_pum… However, I am having difficulty with the onsite and hopping values as I am using TBModels https://github.com/Z2PackDev/TBmodels and therefore the values are not the same for all sites. The problem is that after the scalar values have been passed on to the Builder, these will then be overriden when using functions for the position-dependent Hamiltonian. I tried making a deep copy of the model, which would then serve as a data structure where to draw the scalar values from when calling the Onsite and Hopping functions. The problem with this is a) I am getting a KeyError which I am still not sure why it happens b) It does not feel very memory-efficient. I am wondering if there is another way that this could be done on the Kwant side that I have not been able to think of. Regards -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

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Band Structure in an Electric Field (Lead vs System)
by Shivang Agarwal June 27, 2018

June 27, 2018

Hello All, I am trying to calculate the band structure of my system in the presence of an external electric field. From what I understand, I need to add the electric field as a potential in the onsite energy for the Hamiltonian. Now when I calculate the band structure, I have to use kwant.plotter.bands(sys.leads[0]) to avoid the code throwing up an error. Whereas what I want to be plotting is kwant.plotter.bands(sys), i.e. the band structure of the system and not the leads. The latter method gives an error (code pasted below) of the following kind. TypeError: Expecting an instance of InfiniteSystem. I have also gone through the answer at https://mailman-mail5.webfaction.com/pipermail/kwant-discuss/2016-June/0009… . That code by Anton changes the band structure for different values of electric fields (which is what one would expect), whereas the band structure of sys.leads[0] (in my code) does not change at all even on significantly changing the field. I have a few questions if someone can help me with them. 1) What is the difference between plotting a band structure for sys and sys.leads[0]? 2) How can I plot the band structure of my system (and not its leads) from the code below? Where am I going wrong? How do I avoid the error? *import kwant* *a = 2.46* *lat = kwant.lattice.honeycomb(a = a)* *p, q = lat.sublattices* *def hopping(sitei, sitej):* * return -2.8* *def onsite(site):* * x, y = site.pos* * return -0 + 1*(y)* *def central_region(pos):* * x, y = pos* * return abs(x) < 5*a + 1e-8 and abs(y) < 5*a + 1e-8* *sys = kwant.Builder()* *sys[lat.shape(central_region, (0, 0))] = onsite* *sys[lat.neighbors()] = hopping* *sym = kwant.TranslationalSymmetry((-a, 0))* *lead = kwant.Builder(sym)* *lead[lat.shape(lambda s: abs(s[1]) < 5*a + 1e-8, (0, 0))] = 0* *lead[lat.neighbors()] = hopping* *sys.attach_lead(lead)* *sys.attach_lead(lead.reversed())* *kwant.plotter.bands(sys.finalized().leads[1]) # This works fine* *#kwant.plotter.bands(sys.finalized()) # This throws up an error* Any help would be greatly appreciated! Shivang Agarwal

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Defining orbitals in a 3D structure with 3 basis atoms.
by Sergio Castillo Robles June 21, 2018

June 21, 2018

Hello everyone, i would appreciate any suggestion you could give me to solve this. Well, im trying to create a structure with 3 basis atoms in the unit cell, each atom has a different number of orbitals a=3, b=6 and c=3. I have tried with polyatomic module and creating one lattice for each atom with no success The thing is that i cant figure it out how to create a lattice with different orbitals in each site. I have the on-site and hopping energies matrix so i need to be able to introduce this values. Im pretty new using kwant so any advice is appreciated. Here is the code i've working on (ignore the matrix elements for the moment): import kwant import tinyarray import numpy from matplotlib import pyplot VecPrim = [(3.176, 0, 0), (1.588, 2.7504, 0), (0, 0, 17.49)] base = [(0, 0, 0), (1.588, 0.9168, 0.8745), (0, 0, 1.749)] ### This is the part that i cant get it right, i have tried kwant.lattice.polyatomic ### and defining 3 lattices one for each atom, but no success a = kwant.lattice.general(prim_vecs = VecPrim, basis = (0, 0, 0)) Cpx, Cpy, Cpz, = a.sublattices b = kwant.lattice.general(prim_vecs = VecPrim, basis = (1.588, 0.9168, 0.8745)) xy, xz, yz, x2y2, z2, s = b.sublattices c = kwant.lattice.general(prim_vecs = VecPrim, basis = (0, 0, 1.749)) Npx, Npy, Npz = c.sublattices ### Ignore from here ### def make_cuboid(t=1.0, a=15, b=10, c=5): def cuboid_shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < c syst = kwant.Builder() syst[lat.shape(cuboid_shape, (0, 0, 0))] = 4 * t syst[lat(0, 0, 0)] = numpy.array([[-1.888842, -0.014064-0.000409j, 0.026908+0.003422j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.014064+0.000409j, -1.784936, -0.031384+0.021565j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.026908-0.003422j, -0.031384-0.021565j, 0.710443, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) syst[lat(0, 1, 0)] = numpy.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7.168134, -0.005189-0.047376j, 0.001352+0.000103j, -0.001189-0.00095j, -0.048166-0.007663j, 0.429882+0.00052j, 0, 0, 0], [0, 0, 0, -0.005189+0.047376j, 0.245358, 0.113162-0.072937j, 0.660849-0.06348j, -0.017571+0.035587j, 0.020961-0.017679j, 0, 0, 0], [0, 0, 0, 0.001352-0.000103j, 0.113162+0.072937j, 1.338059, -0.003126-0.016285j, -0.624702-0.065652j, 0.002353+0.001639j, 0, 0, 0], [0, 0, 0, -0.001189+0.00095j, 0.660849+0.06348j, -0.003126+0.016285j, 1.325337, 0.110694+0.01548j, 0.009041+0.004483j, 0, 0, 0], [0, 0, 0, -0.048166+0.007663j, -0.017571-0.035587j, -0.624702+0.065652j, 0.110694-0.01548j, 0.362102, -0.030934+0.002401j, 0, 0, 0], [0, 0, 0, 0.429882-0.00052j, 0.020961+0.017679j, 0.002353-0.001639j, 0.009041-0.004483j, -0.030934-0.002401j, -0.650839, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) syst[lat(0, 0, 1)] = numpy.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3.398186, 0.001839+0.001631j, -0.117366+0.00498j], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.001839-0.001631j, -3.401815, 0.023339+0.009067j], [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.117366-0.00498j, 0.023339-0.009067j, -0.637207]]) syst[lat(0, 0, 1), lat (0, 0, 0)] = ([[0, 0, 0, 0, 0, 0, 0, 0, 0, -1.852931+0.147524j, 0.274586-0.034451j, -0.015051-0.001677j], [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.274338-0.015064j, -1.796449-0.055331j, -0.034396+0.019407j], [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.103127+0.001438j, 0.004816-0.00237j, 3.410475+0.001248j], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1.852931-0.147524j, -0.274338+0.015064j, -0.103127-0.001438j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.274586+0.034451j, -1.796449+0.055331j, 0.004816+0.00237j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.015051+0.001677j, -0.034396-0.019407j, 3.410475-0.001248j, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) syst[lat(0, 1, 0), lat(0, 0, 0)] = ([[0, 0, 0, 0.003644+0.00088j, -0.305706-0.050514j, 0.638425-0.083597j, -1.105645+0.086829j, 1.463462-0.012994j, -0.01338-0.00264j, 0, 0, 0], [0, 0, 0, -0.046131+0.04229j, -1.963829-0.280977j, -1.171301-0.088146j, -1.112788-0.056971j, 0.174769+0.106872j, -0.058159-0.007987j, 0, 0, 0], [0, 0, 0, 0.23188+0.001924j, -0.597505-0.078772j, -0.146976-0.012943j, -0.210584+0.002248j, 0.177022+0.031485j, 0.953363-0.001855j, 0, 0, 0], [0.003644-0.00088j, -0.046131-0.04229j, 0.23188-0.001924j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.305706+0.050514j, -1.963829+0.280977j, -0.597505+0.078772j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.638425+0.083597j, -1.171301+0.088146j, -0.146976+0.012943j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1.105645-0.086829j, -1.112788+0.056971j, -0.210584-0.002248j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1.463462+0.012994j, 0.174769-0.106872j, 0.177022-0.031485j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.01338+0.00264j, -0.058159+0.007987j, 0.953363+0.001855j, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) syst[lat(0, 0, 1), lat(0, 1, 0)] = ([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.184152+0.002778j, 0.321743-0.010571j, 0.183538-0.00067j], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.275145+0.007691j, -0.54144+0.012815j, 0.045847+0.015379j], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.47922+0.015775j, 1.256012+0.007326j, -0.523174+0.00585j], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1.255561-0.002255j, 1.903063+0.010647j, -0.876392+0.010246j], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1.282837-0.091022j, -0.54898+0.001161j, 0.057341-0.004095j], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02765-0.001793j, -0.002902-0.001866j, -0.746426-0.000748j], [0, 0, 0, 0.184152-0.002778j, 0.275145-0.007691j, 0.47922-0.015775j, 1.255561+0.002255j, 1.282837+0.091022j, 0.02765+0.001793j, 0, 0, 0], [0, 0, 0, 0.321743+0.010571j, -0.54144-0.012815j, 1.256012-0.007326j, 1.903063-0.010647j, -0.54898-0.001161j,-0.002902+0.001866j, 0, 0, 0], [0, 0, 0, 0.183538+0.00067j, 0.045847-0.015379j, -0.523174-0.00585j, -0.876392-0.010246j, 0.057341+0.004095j,-0.746426+0.000748j, 0, 0, 0]]) ### 'Till here ##### syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -6 lead = kwant.Builder(kwant.TranslationalSymmetry((-3.176, 0, 0))) def lead_shape(pos): return 0 <= pos[1] < b and 0 <= pos[2] < c lead[lat.shape(lead_shape, (0, 0, 0))] = 4 * t lead[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -6 syst.attach_lead(lead) syst.attach_lead(lead.reversed()) return syst def plot_conductance(syst, energies): data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy) data.append(smatrix.transmission(1, 0)) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() def main(): syst = make_cuboid() kwant.plot(syst) syst = make_cuboid(a=100, b=28, c=4) def family_colors(site): if site.family == d: return 'yellow' elif site.family == e: return 'gray' else: return 'blue' kwant.plot(syst, site_size=0.25, site_lw=0.025, hop_lw=0.05, site_color=family_colors) syst = syst.finalized() plot_conductance(syst, energies=[0.01 * i - 0.3 for i in range(100)]) if __name__ == '__main__': main()

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conservation law
by Prof. CHAN Kwok Sum June 19, 2018

June 19, 2018

Dear Kwant Developers, I understand that a symmetry operator (the conservation law) can be used to block diagonalize the lead hamiltonian, as in the separation of the electrons and holes in superconductors. In the electron-hole case, the symmetry operator is [[-1,0],[0,1]]. There are two eigenvalues (+1, -1) and the eigenvalues are different. Can the kwant code be used to handle a symmetry operator like [[0,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,1]]. There are four eigenvalues in two degenerate pairs. This is like a system with four orbitals in a unit cell and each pair of orbitals have the same energy. There are two possible scenario. With this symmetry operator, the lead Hamiltonian is block diagonalized into two blocks. Can the conservation law function handle this case? What would happen if the hopping can split the degenerate eigenvalues within a single block? Can the conservation law function handle this case too? KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

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Josephson current in a lattice between two superconductors
by Pyykkönen Ville June 15, 2018

June 15, 2018

Hi, I'm trying to use Kwant to investigate behavior of a lattice between two superconductors, namely trying to figure out the Josephson current. The task is basically to diagonalize the related Bogoliubov-de Gennes Hamiltonian and use the eigenvectors and eigenvalues to calculate the current in the lattice. I basically follow the example 2.6. in Kwant documentation to build up the Hamiltonian but let the both leads be superconductors and establish the system in between. I introduce the phase difference between the leads by multiplying the Delta parameter of the other lead by e^(i phi). However, I'm a bit stuck there as I don't know how to utilize the obtained eigenvectors to make wave functions which I could input to t current operator in Kwant. I would really appreciate some help with this or, perhaps, some example code if readily available. Thanks in advance! Regards, Ville Pyykkönen

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AttributeError: 'FiniteSystem' object has no attribute 'site' [site = sys.site(i) not working]
by Shivang Agarwal June 12, 2018

June 12, 2018

Hello All, I am looking to plot the wavefunction (both magnitude and phase on separate plots). The kwant.plotter.map method doesn't give a very appealing look as it plots only in large sized triangles. The kwant.plotter.plot method seems better but I get stuck in one part. There is a piece of code that reads: def family_shape(i): site = sys.site(i) return ('p', 3, 180) if site.family == a else ('p', 3, 0) However, it gives the following error: AttributeError: 'FiniteSystem' object has no attribute 'site' This snippet was taken from online kwant tutorials itself. I am unable to get to the bottom of this error message because the tutorial uses the exact same code. Is there an update to some library of kwant that solves this? Or is there any other way to get better plots for wavefunctions on a system without using the sys.site(i) command? I would like the wave functions to look smooth and continuous. Any help would be appreciated. Best Regards, Shivang -- *Shivang Agarwal* Junior Undergraduate Discipline of Electrical Engineering IIT Gandhinagar Contact: +91-9869321451

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