Mailman 3 July 2021 - Kwant-discuss

Defining uniaxial strain in specified region of graphene
by shrushti.tapar07＠gmail.com 21 Jan '23

21 Jan '23

I want to create the graphene strained superlattice-like structure, having uniaxial strain defined at the specified region. Please, someone can suggest to me how to define the strained region and interface between unstrained and strained graphene regions. Thanks in Advance Shrushti

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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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current-voltage diagram
by loojoo026＠gmail.com 08 Apr '22

08 Apr '22

dear all I have done my project using Kwant and I have drawn a conductance-energy diagram for the system. The question I have is how can I get the current-voltage diagram? thanks Leo

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How the spin is positioned in the Smatrix?
by Qingtian Zhang 07 Mar '22

07 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 07 Mar '22

07 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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Graphene Conductor-Superconductor Conductance above Gap
by Henry Axt 21 Feb '22

21 Feb '22

Hello, I set up a graphene lattice with periodic boundary conditions that is connected to a superconductor (simulated with an electron and hole lattice). When observing the transmission between the electron and hole lattice, I see a small amount conductance above the superconducting gap. I do not see this with something like a square lattice. What could explain this?

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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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module 'kwant.linalg._mumps' has no attribute 'dmumps' ERROR
by BHAVYA BHARDWAJ 02 Sep '21

02 Sep '21

Repected Members, I am a B.Tech Student using Kwant for simulations.Python Version: 3.7.8 Kwant Version: 1.4.2Ubuntu 20The Error I faced is given below. AttributeError Traceback (most recent call last) <ipython-input-6-c80da766c4bb> in <module> 17 pyplot.ylabel("conductance [e^2/h]") 18 pyplot.show() ---> 19 solving(model.tokwant()) <ipython-input-6-c80da766c4bb> in solving(sys) 7 energy = ie * 0.01 8 # compute the scattering matrix at a given energy ----> 9 smatrix = kwant.greens_function(sys, energy,check_hermiticity=False) 10 # compute the transmission probability from lead 0 to 11 # lead 1 ~/Downloads/112358/lib/python3.7/site-packages/kwant/_common.py in inner(*args, **kwargs) 70 if sig.bind(*args, **kwargs).arguments.get(parameter_name): 71 warn() ---> 72 return f(*args, **kwargs) 73 74 return inner ~/Downloads/112358/lib/python3.7/site-packages/kwant/solvers/common.py in greens_function(self, sys, energy, args, out_leads, in_leads, check_hermiticity, params) 485 rhs = sp.bmat([[i for i in linsys.rhs if i.shape[1]]], 486 format=self.rhsformat) --> 487 flhs = self._factorized(linsys.lhs) 488 data = self._solve_linear_sys(flhs, rhs, kept_vars) 489 ~/Downloads/112358/lib/python3.7/site-packages/kwant/solvers/mumps.py in _factorized(self, a) 102 def _factorized(self, a): 103 inst = mumps.MUMPSContext() --> 104 inst.factor(a, ordering=self.ordering) 105 return inst 106 ~/Downloads/112358/lib/python3.7/site-packages/kwant/linalg/mumps.py in factor(self, a, ordering, ooc, pivot_tol, reuse_analysis, overwrite_a) 318 row, col, data) 319 else: --> 320 self.analyze(a, ordering=ordering, overwrite_a=overwrite_a) 321 322 self.mumps_instance.icntl[22] = 1 if ooc else 0 ~/Downloads/112358/lib/python3.7/site-packages/kwant/linalg/mumps.py in analyze(self, a, ordering, overwrite_a) 227 228 if dtype != self.dtype: --> 229 self.mumps_instance = getattr(_mumps, dtype+"mumps")(self.verbose) 230 self.dtype = dtype 231 AttributeError: module 'kwant.linalg._mumps' has no attribute 'dmumps' Kindly guide me so I can overcome this error. Thank You, Regards, Bhavya Bhardwaj

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Quantum Hall Effect in a graphene Hall Bar
by sidsule3000＠hotmail.com 29 Jul '21

29 Jul '21

Hello, I am trying to simulate the quantum hall effect in a hall bar made of a honeycomb (graphene) lattice. I modified the code submitted by C. Groth as a response to a 2015 thread (link below). As soon as I add the vertical leads, I cant seem to get the expected phenomenon for both longitudinal and hall resistances. Here is my code, if anyone spots an error or a solution, do let me know! Sid Sule -------------------------------------------- from cmath import exp import numpy from matplotlib import pyplot import kwant from kwant.digest import gauss def hopping(sitei, sitej, phi, salt): xi, yi = sitei.pos xj, yj = sitej.pos return -exp(-0.5j * phi * (xi - xj) * (yi + yj)) def onsite(site, phi, salt): return 0.05 * gauss(repr(site), salt) def make_system(L=20, W=30): def central_region(pos): x, y = pos return abs(x) < (W/2) and abs(y) < (L/2) lat = kwant.lattice.honeycomb() sys = kwant.Builder() sys[lat.shape(central_region, (0, 0))] = onsite sys[lat.neighbors()] = hopping vertices = numpy.array([[-15, -6, 5, 10], [-15, -6, -10, -5], [6, 15, 5, 10], [6, 15, -10, -5], [-2, 2, 5, 10], [-2, 2, -10, -5]]) for v in vertices: def in_hole(site): x, y = site.pos return (v[0] <= x <= v[1]) and (v[2] <= y <= v[3]) for site in filter(in_hole, list(sys.sites())): del sys[site] sym = kwant.TranslationalSymmetry((-1, 0)) lead = kwant.Builder(sym) lead[lat.shape(lambda s: abs(s[1]) < (L/4), (0, 0))] = 0 lead[lat.neighbors()] = hopping sys.attach_lead(lead) sys.attach_lead(lead.reversed()) edges = numpy.array([[-6, -2, -4], [2, 6, 4]]) for e in edges: sym = kwant.TranslationalSymmetry([0, numpy.sqrt(3)]) lead = kwant.Builder(sym) def lead_region(pos): x, y = pos return (e[0] < x < e[1]) lead[lat.shape(lead_region, (e[2], 0))] = 0 lead[lat.neighbors()] = hopping sys.attach_lead(lead) sys.attach_lead(lead.reversed()) for x in lead.sites(): x.family.norbs = None return sys.finalized() sys = make_system() kwant.plot(sys, site_lw=0.1, lead_site_lw=0, colorbar=False, show=False) energy = 0.35 reciprocal_phis = numpy.linspace(4, 50, 20) current = numpy.array([-1, 1, 0, 0, 0, 0]) r_long = [] r_hall = [] for phi in 1 / reciprocal_phis: params = {"phi": phi, "salt": ""} smatrix = kwant.smatrix(sys, energy, params=params) cond_mat = smatrix.conductance_matrix() # SOLVES FOR V IN I = G*V voltage = numpy.linalg.solve(cond_mat, current) # DIVIDE BY 2 FOR V = I*R, I = 2 r_long.append(abs(voltage[2]-voltage[4]) / 2) r_hall.append((voltage[2] - voltage[3]) / 2) fig, ax = pyplot.subplots(1, 1) ax.plot(reciprocal_phis, r_long) ax.plot(reciprocal_phis, r_hall) fig.show() --------------------- Link of original thread : https://mail.python.org/archives/list/kwant-discuss@python.org/thread/D3MTM…

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3D structure
by tavakkolidjawad 20 Jul '21

20 Jul '21

Dear all In the following code I have defined a three-dimensional structure. The geometry of the lead and the scattering region are the same, but the lead is not ploted as I expected. I expected the lead to have a cubic structure. What is the problem with my code? Thanks Javad tavakoli ############################################################################ ############################################################################ import kwant lat = kwant.lattice.general([(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)], [(0, 0, 10), (0.25, 0.25, 10.25)], name=['a1', 'a2']) a1, a2 = lat.sublattices def make_system(a=10, b=10, c=30): syst = kwant.Builder() def cuboid_shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < 10 syst[a1.shape(cuboid_shape, (0, 0, 0))] = 1 syst[a2.shape(cuboid_shape, (0, 0, 0))] = 1 syst[lat.neighbors()] = 1 def lead_shape(pos): x,y,z = pos return 0 <= x < a and 0 <= y < b and 10 <= z < 25 lead = kwant.Builder(kwant.TranslationalSymmetry((0,0,1))) lead[a1.shape(lead_shape, (0, 0, 10))] = 1 lead[a2.shape(lead_shape, (0, 0, 10))] = 1 lead[lat.neighbors()] = 1 syst.attach_lead(lead) syst.attach_lead(lead.reversed()) return syst , lead def main(): syst,lead= make_system() kwant.plot(syst) syst,lead = make_system(a=1.1, b=1.1, c=1.1) syst.attach_lead(lead) if __name__ == '__main__': main() ###########################################################################

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Kwant-discuss July 2021