Hi,
this is a follow up question to a previous (hijacked?) thread. For completeness I will provide all details, so that no cross referencing is necessary.
I want to compute the electrical conductance of a N-S interface embedded on a hexagonal lattice. The final result should look something like the picture I have attached. The BdG equation is specified in the .pdf.
At the moment I have both particle-hole and spin-up/down degrees of freedom, because later I want to add magnetic fields and such. To attack the problem I have tried to follow the steps outlined in tutorial 2.6 with the addition that I use 4 orbitals and a hexagonal lattice. The conductance should still be given as N - R_{ee,\uparrow} - R_{ee,\downarrow} + R_{he,\uparrow} + R_{he,\downarrow}. Here e, h, \uparrow, and \downarrow refers to electron, hole, spin-up, and spin-down respectively.
In the documentation it says that smatrix.transmission((i, a), (j, b)) gives the transmission from block b of lead j to block a of lead i. I would therefore expect smatrix.transmission((0, 2), (0, 0)) to give me the transmission of an incident electron of spin up in lead 0 to a reflected hole of spin up in lead 0. With this in mind I thought I could write
data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0]-
smatrix.transmission((0, 0), (0, 0)) -
smatrix.transmission((0, 1), (0, 0)) +
smatrix.transmission((0, 2), (0, 0)) +
smatrix.transmission((0,3), (0, 0)))
to compute the conductance. However, doing this gives me an out of bounds error.
As a last resort I tried to write
data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -
smatrix.transmission((0, 0), (0, 0)) +
smatrix.transmission((0, 1), (0, 0)))
as given in the tutorial 2.6. However, this gives me that the conductance is zero.
My question is then, how do I correctly interpret the smatrix.transmission function in my example so that I can compute the correct conductance?
I have attached my code in the .txt file.
Best,
Martin