Mailman 3 May 2017 - Kwant-discuss

Kwant 1.3 has been released
by Christoph Groth 24 May '17

24 May '17

After more than one year of development, we are extremely pleased to announce the release of Kwant 1.3. Kwant 1.3 supports * discretizing of continuum Hamiltonians, * calculating and displaying local densities and currents, * declaring and using symmetries and conservation laws, * calculating bulk properties using the kernel polynomial method, * finalizing builders with multiple translational symmetries, and has many other improvements that are detailed in the "what's new in Kwant 1.3" document [1]. The installation instructions [2] have been updated to explain how to install Kwant 1.3 on computers running GNU/Linux, Mac OS, and Windows. Note that thanks to the package manager Conda it is now much easier to install Kwant under Mac OS and on Unix accounts without root privileges. The new version is practically 100% backwards-compatible with scripts written for previous versions of Kwant 1.x. The Kwant team is happy to welcome Joseph Weston as a member. We are also grateful to the many contributors without whom this release would not be nearly as good: * Jörg Behrmann * Bas Nijholt * Michał Nowak * Viacheslav Ostroukh * Pablo Pérez Piskunow * Tómas Örn Rosdahl * Sebastian Rubbert * Rafał Skolasiński * Adrien Sorgniard We would like to hear your feedback at kwant-discuss(a)kwant-project.org. [1] https://kwant-project.org/doc/1.3/pre/whatsnew/1.3 [2] https://kwant-project.org/install

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Problems with Kwant 1.3 and tinyarray
by Camilla Espedal 24 May '17

24 May '17

Hi again, I had to re-install Kwant 1.3 and tinyarray (dev-version) because of some problems with pip and matplotlib. Anyhow, I can't seem to get it to work, I get the same error that I got earlier when I had installed the wrong version of tinyarray, namely: /usr/local/lib/python3.5/dist-packages/matplotlib-2.0.2+4130.g8ae0dbf-py3.5-linux-x86_64.egg/matplotlib/backends/backend_gtk3agg.py:18: UserWarning: The Gtk3Agg backend is known to not work on Python 3.x with pycairo. Try installing cairocffi. "The Gtk3Agg backend is known to not work on Python 3.x with pycairo. " Traceback (most recent call last): File "/home/camilla/spinHall/Kwant/Tests/spin_kwant13.py", line 45, in <module> syst = make_system(t=1.0, W=10, L=10) File "/home/camilla/spinHall/Kwant/Tests/spin_kwant13.py", line 37, in make_system syst.attach_lead(lead) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 1402, in attach_lead self.leads.append(BuilderLead(lead_builder, tuple(interface))) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 566, in __init__ self.interface = tuple(sorted(interface)) TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int() I run pip show kwant, and pip show tinyarray, and get

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use of a function to define the on-site energy in the leads
by Sebastiano Peotta 24 May '17

24 May '17

Dear developers of Kwant, I have seen most of the examples of Kwant usage, but somehow I miss the usage of functions to define the on-site energy of lattice sites in the leads. I have attached a simple Kwant script which includes the following lines ----------------- sym = kwant.TranslationalSymmetry((0, -1.)) lead = kwant.Builder(sym) lead[lat.shape(region_lead,(0.,0.))] = 4. + potential # use the same potential also for the lead !!! lead[lat.neighbors()] = -1. ------------------ the crucial line is the third one, where the function "potential" that defines the potential in the scattering region is used also in the lead. Since the leads are automatically attached to the scattering region I would expect that the potential is evaluated at the sites where the leads is attached and then repeated according to the translational symmetry given to the lead. Is this the case? I tried to check this using the "map" method in kwant.plotter, but the color in correspondence of the leads is an uninformative grey, which does not belong to the color scale used in the scattering region. Somehow in the documentation I was not able to find what happens when a function is used to define the onsite energy in a lead. Can you fill this gap? Thanks for your help in advance, Sebastiano

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eigenvalues test in wraparound module
by Abbout Adel 15 May '17

15 May '17

Hi All, I am testing the module wraparound and trying to understand how to match the numerical results with the well known formula from literature. I look at the example of graphene given in the module's test [1]: the overall band structure seems fine, but when I try to check a set of eigenvalues for a given (kx,ky) and compare it with the exact formula enclosed below, I fail whatever the parameter 'a' that I choose! The command I use is straightforward: kx,ky=pi/4,pi/6 np.sort(np.linalg.eigvalsh(syst.hamiltonian_submatrix( args + (kx, ky), sparse=False)).real) The only matching I get is for kx,ky=0,0 which means that the problem may be in the choice of the parameter 'a'. for the example in the module a=1/sqrt(3) and seems not to reproduce the expected eigenvalues. Can someone give me some tips ? Thanks in advance. [1] https://gitlab.kwant-project.org/cwg/wraparound/blob/9462edc3c1aee2f391aedf… The formula shown in the figure was obtained from : [2] http://www-personal.umich.edu/~sunkai/teaching/Fall_2013/chapter5.pdf

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Semi-Wrap Around Leads
by John Eaves 10 May '17

10 May '17

Good day, My question today is about how (and if) one can implement semi/partially wrapped around leads in KWANT. I'm unsure of how to do this due to the requirements of periodic boundary conditions, but perhaps one simply needs to be clever and approximate the system in a specific way. What I mean by semi wrapped around leads is illustrated in the following figure http://i.imgur.com/N03MmV9.png (which I have also attached). We have a 3D cuboid shown in white (the idea would be to take a nanowire, but this was easier to draw) and it is deposited on some substrate shown in gray. On top of the cuboid one deposits two leads, which wrap around the three exposed faces and in principle continue outwards; in a physical device they'd end rather soon on one side and continue to some voltage source on the other side. So what I am wondering now is what the closest approximation/most accurate version of this system would be in KWANT. To start with one would of course not need the substrate, that can be left out. Then for the cuboid itself, the scattering region, I suppose one only needs to include the part in which scattering between leads can take part: the section that is covered by the leads, and the part in the middle. So the two outer ends can be cut off. But then the leads. Obviously the 'real' version does not work; the leads need to be infinite, and in reality they are not. One version would be having them be infinite in the y direction; I would define some geometry wrapped around the cuboid, and have it touch only at the ends of the scattering region, while extending outwards to infinity as a hollow shell. This would retain the sort of radial entrance of modes into the cuboid. Would this be a reasonable thing to do? To me it feels a bit wrong as the direction in which the leads are 'long' in the physical device is x, not y. Of course all of the relevant physics of the system does end at the leads in the y-direction, which is why I thought of that approach. But perhaps both x and y should be infinite, or only x. I'm not sure if KWANT will allow this, but maybe the leads could come in from -infinity in the x direction, wrap around the cuboid, and then continue onwards to infinity. This feels a bit problematic in terms of periodicity though. Another option would be ignoring the fact that the leads are wrapped around the cuboid at all; I could simply strip the leads from the scattering region and attach them onto the ends of the cuboid, extending to infinity in the y-directions as a continuation of the scattering region itself. This I am a bit skeptical about, because that makes the modes ' enter' the nanowire in a way that should not be possible in pratice. Say that one introduces some gates into the picture and sets up a field across the wire, it is probable that the outer parts of the wire will have a very different potential than the core, but this lead geometry would simply be able to insert its mode in the center, or at the middle-bottom part. Or am I looking at this the wrong way? Perhaps these effects would be small in any case. And perhaps finally there is a much better option entirely. If you can think of one, I would be very interested in hearing about it. If not, would it be possible to comment on the pro's/cons of the methods I sketch above, and comment on their feasability of implementation? Kind regards John

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Finite bias current
by Arad gold 07 May '17

07 May '17

Hi dear developers, My question is about calculating total current for a finite bias in a nanowire. I looked at the Datta book and try to implement it in KWANT but I can not get a reliable answer, I think I made a mistake somewhere but I can not find it. I define a nanowire and assume that by applying the bias at the ends of that, the energy of each point will decrease linearly. To calculate the current for each bias point I did the following: For each value of bias I change the energy of the system, calculate conductance, and integrate the corresponding conductance from zero(mu left) to energy=bias (mu left). Would you please help me, I don't know what I am doing wrong. Thank you so much, Arad import numpy as np from matplotlib import pyplot import kwant import math from scipy import exp from scipy.integrate import quad #the effective mass for InAs is o.o23m0 and a=1nm t=1.65 L0 = 30 dletaV = 0.025 deltaE = 0.03 beta= 1.0/ 0.025 #becouse of the doping the Fermi level is higher then the conductance band: Ef-Ec= 0.25 delta=0.25 Itot = [] right_fermies = [] right_fermiesEV = [] current=[] def make_system(a=1, t=1.65 , W= 10): lat = kwant.lattice.square(a) sys = kwant.Builder() def bias (site, volt): (x, y) = site.pos if 0 <= x < L0: return (volt /(L0)) * (x) elif x == L0: return (volt) else: return 0 def onsite(site, volt=0): return 4 * t -bias (site, volt) def bias_R (site, volt): (x, y) = site.pos if x == 0: return 4 * t -volt else: return 0 sys[(lat(x, y) for x in range(0,L0) for y in range(W))] = onsite sys[lat.neighbors()] = -t sym_left_lead = kwant.TranslationalSymmetry((-a, 0)) left_lead = kwant.Builder(sym_left_lead) for j in xrange(W): left_lead[lat(0, j)] = 4 * t if j > 0: left_lead[lat(0, j), lat(0, j - 1)] = -t left_lead[lat(1, j), lat(0, j)] = -t sys.attach_lead(left_lead) sym_right_lead = kwant.TranslationalSymmetry((a, 0)) right_lead = kwant.Builder(sym_right_lead) for j in xrange(W): right_lead[lat(0, j)] = bias_R if j > 0: right_lead[lat(0, j), lat(0, j - 1)] = -t right_lead[lat(1, j), lat(0, j)] = -t sys.attach_lead(right_lead) return sys def cal_current (sys, energies, right_fermi): conductance = [] for energy in energies: smatrix = kwant.smatrix(sys, energy, args=[right_fermi]) conductance.append(smatrix.transmission(1,0)) ''' pyplot.figure() pyplot.plot(energies, conductance) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() ''' Iie = 0 intvolt= int((right_fermi)/((deltaE )*t)) for s in xrange(intvolt): #0.77*0.0001 is e^2/h #f_l - fr for conductance[s] F1 = (1.0 / (math.exp((beta)* ((deltaE * s * t ) - delta)) + 1.0)) - ( 1.0 / (math.exp((1.0/ 0.025)*((deltaE * s * t) + right_fermi - delta)) + 1.0)) #f_l - fr for conductance[s+1] F2 = (1.0 / (math.exp((beta)* ((deltaE * (s +1) * t) - delta)) + 1.0 ))-(1.0 / (math.exp((1.0/ 0.025)*((deltaE * (s +1) * t ) + right_fermi - delta)) + 1.0)) H = ((conductance[s]*F1) + (conductance[s +1])*F2)* (deltaE/2) * 0.77 * 0.0001 Iie = H + Iie right_fermiesEV.append(right_fermi ) Itot.append(Iie) right_fermies.append(right_fermi) return Itot def main(): for j in xrange(20): sys = make_system() sys = sys.finalized() #becouse of the doping the integral is not till o (the left Fermi level) it is till 0.25 current = cal_current(sys, energies=[((deltaE * i)) for i in xrange( 25) ], right_fermi= ((dletaV * j))) np.savetxt('Rdatay.dat', Itot) np.savetxt('Rdatax.dat', right_fermies) pyplot.figure() pyplot.plot(right_fermiesEV, current) pyplot.xlabel("bias [ev]") pyplot.ylabel("current [A]") pyplot.show() if __name__ == '__main__': main()

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