Mailman 3 July 2015 - Kwant-discuss

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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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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New instructions for Windows installation
by Michael Wimmer 15 Jan '16

15 Jan '16

Dear kwant users, we have posted new instructions for installing kwant on Windows on the kwant website: http://www.kwant-project.org/install The old instructions do not work any more, as the format of the python packages on Christoph Gohlke's webpage have changed. Best regards, the kwant team

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Package for ubuntu vivid
by David Abergel 17 Sep '15

17 Sep '15

Hi all, firstly, thanks so much for your work in developing and maintaining kwant. Hugely appreciated. Is there any chance you could package it for {,k,x}ubuntu 15.04? I tried installing kwant in that linux today, using the 14.10 package, and I am getting a bunch of errors from Tkinter and matplotlib when I use kwant's inbuilt plotter. Many thanks for your help David

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Re: [Kwant] Spin Currents using Greens Functions
by Joseph Weston 01 Sep '15

01 Sep '15

This time *with* the recipe attached Joe

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SN junction with repulsive interaction in the normal layer
by abhishek kumar 10 Aug '15

10 Aug '15

Hello, I have been trying to understand the conductance for Normal metal-superconductor proximity system with repulsive interaction in the normal layer numerically. The system I intend to solve is a semi-infinite superconductor, located at x<0, in contact with a semi-infinite normal metal with induced superconducting order parameter up to 0<x<d. Both materials are infinite in the direction transverse to the SN interface. The effect of repulsive interaction is that the sign of induced order parameter in the normal layer is opposite to that in the bulk superconductor. The source code for this system is following: import kwant from matplotlib import pyplot def make_system(a=1, t=1.0, W=10, L=30, barrier=1.5, barrierpos=(14, 15), mu=0.4, Delta_N=0.04, Delta_S=0.1, Deltapos_N=9, Deltapos_S=15): lat_e = kwant.lattice.square(a, name='e') lat_h = kwant.lattice.square(a, name='h') sys = kwant.Builder() #### Define the scattering region. #### sys[(lat_e(x, y) for x in range(L) for y in range(W))] = 4 * t - mu sys[(lat_h(x, y) for x in range(L) for y in range(W))] = mu - 4 * t # hoppings for both electrons and holes sys[lat_e.neighbors()] = -t sys[lat_h.neighbors()] = t for i in range(Deltapos_N, L): for j in xrange(W): if i < barrierpos[0]: sys[lat_e(i, j), lat_h(i, j)] = -Delta_N elif i in range(barrierpos[0], barrierpos[1]): sys[lat_e(i,j)] = 4*t + barrier - mu sys[lat_h(i,j)] = mu - 4*t - barrier else: sys[lat_e(i, j), lat_h(i, j)] = Delta_S #### Define the leads. #### # Symmetry for the left leads. sym_left = kwant.TranslationalSymmetry((-a, 0)) # left electron lead lead0 = kwant.Builder(sym_left) lead0[(lat_e(0, j) for j in xrange(W))] = 4 * t - mu lead0[lat_e.neighbors()] = -t # left hole lead lead1 = kwant.Builder(sym_left) lead1[(lat_h(0, j) for j in xrange(W))] = mu - 4 * t lead1[lat_h.neighbors()] = t # Then the lead to the right # this one is superconducting and thus is comprised of electrons # AND holes sym_right = kwant.TranslationalSymmetry((a, 0)) lead2 = kwant.Builder(sym_right) lead2 += lead0 lead2 += lead1 lead2[((lat_e(0, j), lat_h(0, j)) for j in xrange(W))] = Delta_S #### Attach the leads and return the system. #### sys.attach_lead(lead0) sys.attach_lead(lead1) sys.attach_lead(lead2) return sys def plot_conductance(sys, energies): # Compute conductance data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) # Conductance is N - R_ee + R_he data.append(smatrix.submatrix(0, 0).shape[0] - smatrix.transmission(0, 0) + smatrix.transmission(1, 0)) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() kwant.plotter.bands(sys.leads[0]) def main(): sys = make_system() # Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() plot_conductance(sys, energies=[0.002 * i +0.00001 for i in xrange(100)]) if __name__ == '__main__': main() I expect a peak in the conductance at zero energy. Now the question I am having here is that I am able to observe the peak when chemical potential (\mu) is of the order of bulk superconducting order parameter (Delta_S) which is unphysical. Also, I must have induced order parameter in the normal layer (Delta_N) much smaller than bulk superconducting order parameter. Can you suggest me something on that? I have analytical results for this type of system and I just want agreement of the same from numerics. Thanks Abhishek -- -- Abhishek Kumar Department of Physical Sciences University of Florida, Gainesville FL 32608 Alternate e-mail ID - kumarabhi(a)ufl.edu Mobile - +1-3522831740 "Life isn't about how to survive the storm, but how to dance in the rain," - Unknown

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stabilized evanescent modes in the lead
by Sergey 10 Aug '15

10 Aug '15

Dear Developers, I am a bit surprised that for my system with 16 sites and 9 hoppings between the unit cells I get lead.modes(E, args =[...] ) returning stabilized modes which are 9 vectors of length 9 . I understand that my hopping is degenerate and what I hoped to get from calling lead.modes(E, args =[...] ) is evanescent mode vectors of length 16 with corresponding complex momenta and some extra vectors spanning the non-propagating subspace. Could you clarify how to get what I want, please. Best wishes, Sergey

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Extracting data from each lattice (spin up and down)
by Gerson 10 Aug '15

10 Aug '15

I'm trying to reproduce the data from PRB 74, 205307 (2006) with Kwant. I'm having trouble extracting data from the spin up and spin down lattices. This is how I do it: Define two square lattices with names "up" and "down". Here's the code for the local energies: lat_up = kwant.lattice.square(1, name="up") lat_dw = kwant.lattice.square(1, name="dw") delta=1.1*Ny; sys[(lat_up(x, y) for x in range(Nx) for y in range(Ny))] = 4*t sys[(lat_dw(x, y+delta) for x in range(Nx) for y in range(Ny))] = 4*t I'm using this "delta" so that the kwant.plot(sys) show then separately. Define separate leads for the spin up and down lattices. So I can investigate the injection of each kind of spin. To reproduce Fig.1, panels (b) and (c), of the paper above I run rho0=np.abs(wf(0).sum(axis=0))**2 This gives me the spin up and down projections of the wave-function injected via lead 0 (up lead). But the spin up projection is on one lattice, while the spin down is on the other lattice. When I plot using kwant's map plot (command below), I do see exactly Fig.1(b) and (c), one in each lattice. kwant.plotter.map(sys, rho0); But I don't know how to extract from rho0 (or from kwant's wave-function command) the data from a given lattice. When I try to implement a spin-orbit Hamiltonian using matrices instead of separate lattices, it is easy to split the spin up and down data using something like ldos[0::2] and ldos[1::2], since the up and down data alternate in the array. But with matrices I have no control over the spin up or down injection. So it seems that I do have to use separate lattices. So, with separate lattices... how do I extract the data from each lattice to separate arrays? Thanks in advance, Best regards, Gerson

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Nearest neighbor Hamiltonian elements (Current density maps)
by LaGasse, Samuel 01 Aug '15

01 Aug '15

Hi All, I am currently trying to implement the advice given by Joseph in https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00075.html? to write a code which generates the current density going into each site in my graphene system. My issue is with returning the nearest neighbor hopping elements in graphene. In the example Joseph posted for a square lattice, there is an obvious coordinate for the nearest neighbor sites. It seems to me that in graphene (or any honeycomb lattice), this is not so obvious. I have been looking for a function built into Kwant that would give me what I need, but haven't had much luck. I've figured out lots of ways (for example, using sys_leads_sites on my finalized system) to generate the number assigned to each site and the corresponding position, but not a good way to determine which are nearest neighbors. I'm guessing the answer is very simple using some of the machinery built into Kwant, I'm just not seeing it. Does anyone have any tips they would be willing to give me? I am not looking for a complete current density code, just a nudge in the right direction. ? Thanks very much! Sam

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defining hopping in the lead
by Sergey 31 Jul '15

31 Jul '15

Dear Developers, Could you help with defining the hopping in the lead, please. My problem is that in the non-finalized system, sites() contains only one copy on the lead unit cell and I fail to write a correct hopping that would make the lead connected. Here's an example of the hopping function that works for finite system but results in disconnected system for the lead. def crit(site1,site2): diff = site1.pos-site2.pos pr=np.dot(diff,symvecty) diff1= diff - symvecty*(int(pr/np.dot(symvecty,symvecty)+0.001+1000)-1000) [x,y,z] = diff1 if 0.9<abs(z)<1.1 and abs(y)<0.1 and abs(x)<0.1: return True else: return False def connect(sys,crit): result=[] for site1 in sys.sites(): for site2 in sys.sites(): if crit(site1,site2): result.append((site1,site2)) return iter(result) lead[connect(lead,crit)] = tz Best wishes, Sergey

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Kwant-discuss July 2015