Dear Camilla, Could the difference originate from you using a lattice constant of 2 instead of 1?
Anton On Tue, Jan 24, 2017, 10:41 Camilla Espedal <camilla.espe...@ntnu.no> wrote: > Dear Anton, > > Thanks again for all your help. I will try to do it the linux way. Just > one more thing regarding this. I wrote a script in the old Kwant to find > the total conductance and compare it to the one in your notebook. While the > two plots are qualitatively similar, they are not the same. Am I missing > something, or am I calculating different things? > > Best, Camilla > > (my code): > > # Tutorial 2.3.1. Matrix structure of on-site and hopping elements > # ================================================================ > # > # Physics background > # ------------------ > # Gaps in quantum wires with spin-orbit coupling and Zeeman splititng, > # as theoretically predicted in > # http://prl.aps.org/abstract/PRL/v90/i25/e256601 > # and (supposedly) experimentally oberved in > # http://www.nature.com/nphys/journal/v6/n5/abs/nphys1626.html > # > # Kwant features highlighted > # -------------------------- > # - Numpy matrices as values in Builder > > import kwant > > # For plotting > import matplotlib.pyplot as plt > > # For matrix support > import tinyarray > import numpy as np > > # define Pauli-matrices for convenience > 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]]) > > > def make_system(a=2, t=1.0, alpha=0.1, e_z=0.05, W=10, L=10): > # Start with an empty tight-binding system and a single square lattice. > # `a` is the lattice constant (by default set to 1 for simplicity). > lat = kwant.lattice.square(a) > > sys = kwant.Builder() > > #### Define the scattering region. #### > 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 range(W))] = 4 * t * sigma_0 > # hoppings in x-direction > lead[lat.neighbors()] = \ > -t * sigma_0 > > #### Attach the leads and return the finalized system. #### > sys.attach_lead(lead) > sys.attach_lead(lead.reversed()) > > return sys > > > def plot_conductance(sys, energies): > # Compute conductance > data = [] > for energy in energies: > smatrix = kwant.smatrix(sys, 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(): > sys = make_system() > > # Check that the system looks as intended. > kwant.plot(sys) > > # Finalize the system. > sys = sys.finalized() > energies = np.linspace(0, 1, 200) > smatrices = [kwant.smatrix(sys, energy) for energy in energies] > > fig = plt.figure(figsize=(13, 8)) > ax = fig.add_subplot(1, 1, 1) > > ax.plot(energies, [smatrix.transmission(1,0) for smatrix in > smatrices], label='total') > > ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') > ax.set_xlabel('$E/t$', fontsize='xx-large') > ax.legend(fontsize='x-large') > > plt.show() > > > > # Call the main function if the script gets executed (as opposed to > imported). > # See <http://docs.python.org/library/__main__.html>. > if __name__ == '__main__': > main() > > -----Original Message----- > From: anton.akhme...@gmail.com [mailto:anton.akhme...@gmail.com] On > Behalf Of Anton Akhmerov > Sent: 17. januar 2017 10:48 > To: Camilla Espedal <camilla.espe...@ntnu.no> > Cc: kwant-discuss@kwant-project.org > Subject: Re: [Kwant] Regarding smatrix and spin > > Dear Camilla, > > It seems that you are trying to install Kwant on windows. This is a very > hard task, and I fear none of the Kwant developers has enough knowledge of > it right now (our Windows packages are built by Christoph Gohlke, see [1] > for the build environment description). However if you are using windows > 10, I suggest to try to install Kwant using the windows subsystem for > linux. That way the standard Ubuntu build procedure should work for you. > > Best, > Anton > > [1]: http://www.lfd.uci.edu/~gohlke/pythonlibs/ > > On Mon, Jan 16, 2017 at 9:45 AM, Camilla Espedal <camilla.espe...@ntnu.no> > wrote: > > Thanks a lot. I tried to install the cons_laws_combined, but I get the > following error message: > > > > "LINK: fatal error LNK1181: cannot open input file 'lapack.lib'" > > > > Is there some package or installation I am missing? > > > > Best regards, > > Camilla > > > > -----Original Message----- > > From: anton.akhme...@gmail.com [mailto:anton.akhme...@gmail.com] On > > Behalf Of Anton Akhmerov > > Sent: 8. januar 2017 16:35 > > To: Tómas Örn Rosdahl <torosd...@gmail.com> > > Cc: Camilla Espedal <camilla.espe...@ntnu.no>; > > kwant-discuss@kwant-project.org > > Subject: Re: [Kwant] Regarding smatrix and spin > > > > Hi Camilla, everyone, > > > > I've slightly modified Tómas's example to a case where the spins do get > coupled, check it out: > > http://nbviewer.jupyter.org/url/antonakhmerov.org/misc/spin_conductanc > > e.ipynb > > > > I've also provided more detailed installation instructions in the > notebook. > > > > Cheers, > > Anton > > > > On Sun, Jan 8, 2017 at 2:45 PM, Tómas Örn Rosdahl <torosd...@gmail.com> > wrote: > >> Dear Camilla, > >> > >> For a Hamiltonian with degeneracies due to a conservation law, the > >> scattering states will in general not have a definite value of the > >> conservation law. In your case, Kwant returns scattering states that > >> are arbitrary linear combinations of spin up and down, so it is not > >> possible to label the amplitudes in the scattering matrix by spin. > >> > >> However, in Kwant 1.3 a feature will be added that allows for the > >> construction of scattering states with definite values of a > >> conservation law. See here for an explanation of the basic idea behind > the algorithm. > >> > >> We're currently working on implementing this feature in Kwant itself. > >> The good news is that we're practically done - here is a link to a > >> git repo with a functioning implementation. After you clone the repo, > >> check out the branch cons_laws_combined, which contains a version of > >> Kwant with conservation laws implemented. This notebook contains a > >> simple example to illustrate how to work with conservation laws and the > scattering matrix. > >> > >> I invite you and anyone else who is interested to give it a try. We'd > >> appreciate any feedback! > >> > >> In your case specifically, there would be two projectors in the new > >> implementation - P0 which projects out the spin up block, and P1 that > >> projects out the spin down block. If they are specified in this > >> order, then the spin up and down blocks in the Hamiltonian have block > >> indices > >> 0 and 1, respectively. In the new implementation, it is possible to > >> ask for subblocks of the scattering matrix relating not only any two > >> leads, but also any two conservation law blocks in any leads. To get > >> the reflection amplitude of an incident spin up electron from lead 0 > >> into an outgoing spin down electron in lead 0, you could simply do > >> smat.submatrix((0, 1), (0, 0)). Here, the arguments are tuples of > indices (lead index, block index). > >> > >> Best regards, > >> Tómas > >> > >> On Fri, Jan 6, 2017 at 3:46 PM, Camilla Espedal > >> <camilla.espe...@ntnu.no> > >> wrote: > >>> > >>> Hi again, > >>> > >>> > >>> > >>> This question is basically the same as this: > >>> https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg0007 > >>> 6 > >>> .html > >>> > >>> > >>> > >>> I want to calculate some things using the scattering matrix. I > >>> started out with a very simple system, most basic two-terminal > >>> system. For some energy there is one propagating mode. I now add > >>> matrix structure to the mix (just multiply by s_0 everywhere) and > >>> there are now 2 propagating modes (which makes sense). > >>> > >>> > >>> > >>> Now, if I look at the reflection coefficients for lead 0 by using > >>> submatrix(0,0), it is now a 2x2 matrix after I introduced the > >>> matrices. How are the elements ordered? Is it > >>> > >>> > >>> > >>> [[r_upup, r_updown],[r_downup, r_downdown]] > >>> > >>> > >>> > >>> I know that I could make two lattices, but since I do not plan to > >>> use the other functions such as transmission. I just want the smatrix. > >>> > >>> > >>> > >>> Hope you can help me, and thanks in advance. > >>> > >>> > >>> > >>> Best regards, > >>> > >>> Camilla > >> > >> >
