Mailman 3 July 2021 - Kwant-discuss

Quantum Hall Effect in a graphene Hall Bar
by sidsule3000＠hotmail.com July 29, 2021

July 29, 2021

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 July 19, 2021

July 19, 2021

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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only lowest bands with kwant.physics.Bands
by Vardan Kaladzhyan July 17, 2021

July 17, 2021

Dear Kwant Developers, I am using kwant.physics.Bands to obtain the bands for a three-dimensional setup with one 'momentum'. Hence, I am inserting a set of momenta and getting a set of energies for each momentum. Is there a way to ask Kwant to only compute the lowest bands? My system is quite large and calculating all the bands is extremely time-consuming. Thank you! Cheers, Vardan.

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wave_function(...) returns array of size 0 when norbs=1
by Derek Reitz July 13, 2021

July 13, 2021

Hello Kwant community, I am trying to use kwant.wave_function(...) on a system with norbs=1. For example, if I try to plot the wave function in the Kwant example file quantum_wire.py (which may be found here https://kwant-project.org/doc/1.0/_downloads/quantum_wire.py ), I get an error: "vector is incorrect shape." The code to plot the wave function is: wf = kwant.wave_function(sys,energy=0)(0) rho = kwant.operator.Density(sys) density = rho(wf) kwant.plotter.density(sys, density) When I do print(np.shape(wf)) I get (0, 300); where 300 is the number of sites in this example lattice. Thus it seems like the wave function information might be contained in the returned object, but I am not sure how to access it. Please let me know if you have any idea on what I am doing incorrectly here. Thank you, Derek

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Current Density in bilayer graphene
by mohamad.mirzakhani＠gmail.com July 13, 2021

July 13, 2021

Dear all, I have written a code in Kwant for a bilayer graphene quantum dot (in 2D manner) to calculate some electronic properties. I can get the results correctly for, e.g, conductance, spectrum, and LDOS. But there is a problem in plotting CURRENT density and I get the following error. ~~ need at least one array to concatenate Has anyone had a similar experience ? The current density part of code is: ________________________________________________________________ ### Current plot params = dict(B=Bfield, r0=[0,0], h0=0) wf = kwant.wave_function(syst, energy=0.01, params=params) psi = wf(0)[0] J_0 = kwant.operator.Current(syst) current = J_0(psi, params=params) kwant.plotter.current(syst, current) _________________________________________________________________

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Capability and limitations of KWANT
by henadeerapb＠gmail.com July 9, 2021

July 9, 2021

Dear all, My systems consist around 4000 Si atoms. Would KWANT be capable of handling such a system when my computational resources are limited to 64GB of memory? Note: I am studying the thermal properties across Si nanoparticle junctions for my postgraduate research. Even though I am interested in looking into the electrical properties in these structures as well, it is my understanding that DFT codes such as Quantum Espresso and VASP are the most commonly used programs for this type of application. However, as a single Si nanoparticle junction would contain around 4000 atoms (5nm diameter nanoparticle), these DFT based approaches are not feasible considering the fact that I have access to limited computational resources. This is when I came across the KWANT package which appears to be capable of handling such systems. However, I would like to confirm the following before I dive in and spend my time studying the software package. I would appreciate any helpful replies in this regard. Thank you

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Custom sublattices for a noncrystalline lattice
by Victor Regis July 2, 2021

July 2, 2021

Dear all, I have a custom lattice that I generate outside of Kwant and I want specific sites to belong to specific sublattices. As a minimal reproducible example suppose I have a square lattice (evidently, this is a crystalline lattice and there are simple ways to do this in Kwant, but take this lattice just as the simplest example): lattice = np.array([[x,y] for x in range(20) for y in range(20)]) And I set the system: def system(basis,size): syst = kwant.Builder() lat = kwant.lattice.general([(0,size),(size,0)],basis = basis,norbs=1) #then the onsite and hoppings etc return syst.finalized() I know that lat is automatically split into 400 sublattices (one for each lattice site) but what I want is, for example, to make every other site be of sublattice family "b" and the rest of "a" and things along those lines. Is there a simple way to implement this? I imagine that implementing a separate class can do the trick, but it seems more complicated than it should be. Also, I reckon I could instantiate each sublattice as a different lattice.general and go from there, but again, it doesn't feel like the proper way to implement it. In short, I want to make a lattice.general lattice from a custom basis of N-atoms and I want to specify which sites belong to which sublattices. Thanks in advance.

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