Dear Lorenzo,
What you have explained is not enough to be of help. Meanwhile, I think it useful to have a look at previous discussions regarding using the conservation law to easily compute the spin conductance Ref*.
You see bello a small script that might be useful:
syst = kwant.Builder()
sym = kwant.TranslationalSymmetry(lat.vec((-1, 0)))
syst = kwant.Builder(sym, conservation_law=-sigma_z)  
smatrix = kwant.smatrix(syst.finalized(), energy, args=(params,))
# the spin up conductance (up to up)
Gup.append(smatrix.transmission((1, 0), (0, 0)))
# the spin down conductance (down to down)
Gdn.append(smatrix.transmission((1, 1), (0, 0)))
# total conductance
G.append(smatrix.transmission((1, 0), (0, 0))+smatrix.transmission((1, 1), (0, 0)))


best; Adel

Le mer. 6 mars 2024 à 16:53, Lorenzo BAGNASACCO <> a écrit :
Hi everyone! I am a beginner Kwant consumer and, for this reason, I am trying to "solve" very simple problems, i.e. problems for beginners. The first one is the following:

I have a 1D problem where basically a spin-1/2 particle crosses a region without a potential neither magnetic fields. I am able to write correctly the setup of the problem in Kwant. Fixed the incoming particle energy, I find a 4 by 4 scattering matrix (this is comforting), but I do not understand which is the protocol that Kwant uses to order the coefficients in the scattering matrix. For example, according to the usual description of the transmission matrix (from left-to-right), the element t_{00} corresponding to the probability to start, for example, in the state s=-1/2 in the left lead and arrives in the state s=-1/2 in the right lead, and similarly for the other elements. How can I manage these labeling in my code?

Thank you!