Mailman 3 February 2017 - Kwant-discuss

How the spin is positioned in the Smatrix?
by Qingtian Zhang March 6, 2022

March 6, 2022

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 March 6, 2022

March 6, 2022

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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How to caculate hall resistance
by ZHANG Bing Sept. 12, 2021

Sept. 12, 2021

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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(no subject)
by enrique colomes March 10, 2017

March 10, 2017

Hello, My name is Enrique and first of all, thanks for the developping of such a useful tool. My question is related to that one of the edge potentials. I am trying to reproduce the Haldane model with disorder in a rectangular scattering region. My goal is to introduce edge disorder as well as compute the local current density. I have two problems: a) Regarding the edge disorder, I cannot remove the disorder in the edges with the leads (I saw your recent previous discussion) b) Is it possible already to compute directly from Kwant the local current density? If yes, how? Thanks again, Enrique from __future__ import division # so that 1/2 == 0.5, and not 0 from scipy.sparse import spdiags from math import pi, sqrt, tanh, e import numpy as np import kwant import random import math # For computing eigenvalues import scipy.sparse.linalg as sla # For plotting from matplotlib import pyplot # Define the graphene lattice graphene = kwant.lattice.honeycomb() a, b = graphene.sublattices edge_potential=10 def make_system(L=10, W=10, pot=0.001): t=1 tt= 0.04 * t phi=1*pi/2 edge=1 # 1 if there is edge disorder bulk=0 # 1 if there is bulk disorder nnn_hoppinga=tt*e**(1j*phi) nnn_hoppingb=tt*e**(1j*phi) #### Define the scattering region. #### def rec(pos): x, y = pos return 0 < x < L and 0 < y < W sys = kwant.Builder() # w: width and pot: potential maximum of the p-n junction def potential(site): (x, y) = site.pos d = y * 2 + x * 3 return 0 sys[graphene.shape(rec, (1, 1))] = potential # specify the hoppings of the graphene lattice nn_hoppings = (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b)) nnn_hoppings_a = (((-1, 0), a, a), ((0, 1), a, a), ((1, -1), a, a)) nnn_hoppings_b = (((1, 0), b, b), ((0, -1), b, b), ((-1, 1), b, b)) sys[[kwant.builder.HoppingKind(*hopping) for hopping in nn_hoppings]] = -t sys[[kwant.builder.HoppingKind(*hopping) for hopping in nnn_hoppings_a]] = -nnn_hoppinga sys[[kwant.builder.HoppingKind(*hopping) for hopping in nnn_hoppings_b]] = -nnn_hoppingb # Modify the scattering region if edge==1: # change the values of the potential at the edge for site in sys.expand(graphene.shape(rec, (0, 1))): if sys.degree(site)<=9 and abs(site.pos[0])!=L-4: #abs(site.pos[0])!=19 execludes the interfaces with the leads sys[site]=edge_potential elif bulk==1: # change the values of the potential at the edge for site in sys.expand(graphene.shape(rec, (0, 1))): if sys.degree(site)==9 and abs(site.pos[0])!=19: #abs(site.pos[0])!=19 execludes the interfaces with the leads sys[site]=edge_potential #### Define the leads. #### # left lead sym0 = kwant.TranslationalSymmetry(graphene.vec((-1, 0))) sym0.add_site_family(graphene.sublattices[0], other_vectors=[(-1, 2)]) sym0.add_site_family(graphene.sublattices[1], other_vectors=[(-1, 2)]) def lead0_shape(pos): x, y = pos return (0 < y < W) lead0 = kwant.Builder(sym0) lead0[graphene.shape(lead0_shape, (0, 0))] = -pot lead0[[kwant.builder.HoppingKind(*hopping) for hopping in nn_hoppings]] = -t lead0[[kwant.builder.HoppingKind(*hopping) for hopping in nnn_hoppings_a]] = -nnn_hoppinga lead0[[kwant.builder.HoppingKind(*hopping) for hopping in nnn_hoppings_b]] = -nnn_hoppingb # right lead sym1 = kwant.TranslationalSymmetry(graphene.vec((1, 0))) sym1.add_site_family(graphene.sublattices[0], other_vectors=[(-1, 2)]) sym1.add_site_family(graphene.sublattices[1], other_vectors=[(-1, 2)]) def lead1_shape(pos): x, y = pos return (0 < y < W) lead1 = kwant.Builder(sym1) lead1[graphene.shape(lead1_shape, (0, 0))] = pot lead1[[kwant.builder.HoppingKind(*hopping) for hopping in nn_hoppings]] = -t lead1[[kwant.builder.HoppingKind(*hopping) for hopping in nnn_hoppings_a]] = -nnn_hoppinga lead1[[kwant.builder.HoppingKind(*hopping) for hopping in nnn_hoppings_b]] = -nnn_hoppingb sys.attach_lead(lead1) sys.attach_lead(lead0) return sys # Call the main function if the script gets executed (as opposed to imported). if __name__ == '__main__': main()t.show() def main(): sys = make_system() # Check that the system looks as intended. def family_color(site): #print(sys[site]) if sys[site]==edge_potential: return 'green' else: return 'black' def site_size(site): if sys[site]==edge_potential: return 0.35 else:return 0.2 kwant.plot(sys,site_color=family_color,site_size=site_size) # Finalize the system. sys = sys.finalized() # Compute number of neighbors i=sys.sites.index(graphene(5,6)) all_the_neighbors=sys.graph.out_neighbors(i) # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html><http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main()

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seg fault at test run on CentOS
by Fatih Dogan Feb. 28, 2017

Feb. 28, 2017

Hello, I have installed the latest version of kwant on a CentOS system that I do not have root access. So I installed it on my home directory. When I run the test file, i get the following seg fault. python3 -c 'import kwant; kwant.test(verbose=2)' /lib/python3.6/site-packages/kwant-unknown-py3.6-linux-x86_64.egg/kwant/solvers/default.py:18: RuntimeWarning: MUMPS is not available, SciPy built-in solver will be used as a fallback. Performance can be very poor in this case. "Performance can be very poor in this case.", RuntimeWarning) kwant.graph.tests.test_core.test_empty ... ok kwant.graph.tests.test_core.test_num_nodes ... ok .... kwant.tests.test_lattice.test_neighbors ... ok kwant.tests.test_lattice.test_shape ... ok kwant.tests.test_lattice.test_wire ... ok kwant.tests.test_lattice.test_translational_symmetry ... Segmentation fault Where I skipped a lot of lines, they were ok for most, skipped when related to MUMPS. I am not that familiar with python or kwant to know what this error means. Can someone help? Thanks Fatih

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Transport across infinite plane with wraparound module
by Kristjan Eimre Feb. 26, 2017

Feb. 26, 2017

Hello Kwant community, I am trying to model transport across an infinite potential barrier plane with the wraparound module. My current code is here: http://pastebin.com/ ux1PwvXS I have been trying to follow the guidance provided in this comment: https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00873.html The system setup is simple, it has a rectangular finite width (in x direction) barrier with potential V0 with a hole in the middle with potential V_hole. In y direction, the barrier is periodic (so the holes are infinitely repeating). I hope that this is correctly implemented in the code. The wraparound module is used on this barrier, making the system finite in y direction and creating a new parameter called ky. I have multiple questions about the parameter ky, leads and the physics. See the attached figure system_schematic.pdf for visual illustration. 1) First of all, I suspect that infinitely wide leads (somehow by using additional translational symmetry for leads and the wraparound module), which would result in plane waves without the transversal energy quantization are not possible. Is this correct? Ideally I would like the result to be independent of the y position of the potential barrier hole (i.e. independent of the hole_y variable). 2) If I calculate transmission for a given energy value, is the k vector of the incoming electron wave (and thus the "effective" orientation of the lead) given by k=(kx, ky), where kx is given such that the specified energy is obtained (taking into account that the transversal quantization energy is subtracted for a given mode)? 3) Is the reflection and transmission calculated only in the direction of the leads and the reflection and transmission in arbitrary directions is not taken into account (see figure for details)? I apologize if the questions are basic or unclear, hopefully you can give some insight into the problem or tell me if I have fundamentally misunderstood something. Best regards, Kristjan

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Re: [Kwant] How to attach the leads manually?
by Татьяна Григоренко Feb. 20, 2017

Feb. 20, 2017

TranslationalSymmetry does not work with my SimpleSite Family. Therefore, I attach the leads manually. I Use class kwant.builder.BuilderLead(builder, interface). I define a builder in the following way: #The tight-binding system of a left lead. left_lead = kwant.Builder() #Add sites lead left_lead[lat(x1, y1)] = 1.5 left_lead[lat(x2, y2)] = 1.5 etc #Add hoppings left_lead[lat(x2, y2), lat(x1, y1)] = 2j etc The same way I define the interface(wich called left_sequence) but without the hoppings. l_lead = kwant.builder.BuilderLead(left_lead, left_sequence). But it does not work. Where I'm wrong? As the lead I want to use the left and right boundary of my graphene atoms. С уважением, Татьяна Григоренко

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Smatrix in hall bar
by Ali Asgharpour Feb. 15, 2017

Feb. 15, 2017

Hello all, I have a question about one of the functions in this link: https://nbviewer.jupyter.org/url/topocondmat.org/notebooks/w3_pump_QHE/Laug… For plotting Hall conductance and longitudinal one, there is a section where you defined a G function, which I put it below: def G(syst, p): smatrix = kwant.smatrix(syst, args=[p]) G = [[smatrix.transmission(i, j) for i in range(num_leads)] for j in range(num_leads)] G -= np.diag(np.sum(G, axis=0)) return calculate_sigmas(G) I want to know why we need this line " G -= np.diag(np.sum(G, axis=0)) " since G matrix is already calculated in the previous line? Your time and consideration are greatly appreciated. Best regards, Ali

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Using Kwant for finding tunneling probability from metal to vacuum
by Kristjan Eimre Feb. 14, 2017

Feb. 14, 2017

Hello Kwant experts, I have studied Kwant a bit, but before I delve deeper into it, I want to know if it can be applied to my problem. I have a 3d electron potential landscape for a metal-vacuum surface calculated with DFT. (More detailed info and pictures in [1]). Can I use Kwant to calculate the transmission probability of electrons incident on the surface? And if kwant is not suitable for this problem, perhaps you know of any other numerical software or method that would allow this calculation? [1] - http://physics.stackexchange.com/questions/295329/quantum-tunneling-probabi… Best regards, Kristjan

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Re: [Kwant] Regarding smatrix and spin
by Camilla Espedal Feb. 14, 2017

Feb. 14, 2017

Dear Anton, sorry for troubling you again. so I finally got hold of a linux-computer, and managed to run the commands and install all the things in the notebook. When I try to run the code you have in your notebook however, I get the following error message: File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 1371, in attach_lead self.leads.append(BuilderLead(lead_builder, tuple(interface))) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 565, in __init__ self.interface = tuple(sorted(interface)) TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int() Do you know what the problem could be? Best, Camilla The code if needed: import kwant import tinyarray as ta import numpy as np from scipy import sparse from matplotlib import pyplot import matplotlib s0 = ta.array([[1, 0], [0, 1]]) sx = ta.array([[0, 1], [1, 0]]) sy = ta.array([[0, 1j], [-1j, 0]]) sz = ta.array([[1, 0], [0, -1]]) # Adapted from https://kwant-project.org/doc/1/tutorial/tutorial2 def make_system(t=1.0, W=10, L=10): # Now we must specify the number of orbitals per site. lat = kwant.lattice.square(norbs=2) syst = kwant.Builder() syst[(lat(x, y) for x in range(L) for y in range(W))] = \ lambda s, alpha, E_z: 4 * t * s0 + E_z * sz syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 - 1j * alpha * sy syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ lambda s1, s2, alpha, E_z: -t * s0 + 1j * alpha * sx # The new bit: specifying the conservation law. lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)), conservation_law=-sz, time_reversal=s0) lead[(lat(0, j) for j in range(W))] = 4 * t * s0 lead[lat.neighbors()] = -t * s0 # Note: no spin-orbit in the lead. syst.attach_lead(lead) syst.attach_lead(lead.reversed()) syst = syst.finalized() return syst syst = make_system(t=1.0, W=10, L=10) energies = np.linspace(0, 1, 200) smatrices = [kwant.smatrix(syst, energy, args=(0.2, 0.05)) for energy in energies] fig = pyplot.figure(figsize=(13, 8)) ax = fig.add_subplot(1, 1, 1) # Like previously smatrix.transmission(lead1, lead0) is transmission from lead0 to lead1 ax.plot(energies, [smatrix.transmission(1, 0) for smatrix in smatrices], label='total') # The new bit: smatrix.transmission((lead1, q1), (lead0, q0)) is the transmission from the # q0 block of the lead0 into the q1 block of lead1. The subblock ordering is same as we used # in set_symmetry. ax.plot(energies, [smatrix.transmission((1, 0), (0, 0)) for smatrix in smatrices], label='$G_{↑↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 0)) for smatrix in smatrices], label='$G_{↑↓}$') ax.plot(energies, [smatrix.transmission((1, 0), (0, 1)) for smatrix in smatrices], label='$G_{↓↑}$') ax.plot(energies, [smatrix.transmission((1, 1), (0, 1)) for smatrix in smatrices], label='$G_{↓↓}$') ax.set_ylabel('$G [e^2/h]$', fontsize='xx-large') ax.set_xlabel('$E/t$', fontsize='xx-large') ax.legend(fontsize='x-large'); On 24. jan. 2017 13:18, Anton Akhmerov wrote: OK, please double-check the remaining simulation parameters. Anton On Tue, Jan 24, 2017 at 1:00 PM, Camilla Espedal <camilla.espedal(a)ntnu.no> wrote: Dear Anton, I triend changing it, but that does not solve the problem. Best, Camilla From: Anton Akhmerov [mailto:anton.akhmerov+kd@gmail.com] Sent: 24. januar 2017 12:36 To: Camilla Espedal <camilla.espedal(a)ntnu.no> Cc: kwant-discuss(a)kwant-project.org Subject: Re: [Kwant] Regarding smatrix and spin 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.espedal(a)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.akhmerov(a)gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 17. januar 2017 10:48 To: Camilla Espedal <camilla.espedal(a)ntnu.no> Cc: kwant-discuss(a)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.espedal(a)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.akhmerov(a)gmail.com [mailto:anton.akhmerov@gmail.com] On Behalf Of Anton Akhmerov Sent: 8. januar 2017 16:35 To: Tómas Örn Rosdahl <torosdahl(a)gmail.com> Cc: Camilla Espedal <camilla.espedal(a)ntnu.no>; kwant-discuss(a)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 <torosdahl(a)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.espedal(a)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

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