Dear all,
as is explained in
https://kwant-project.org/doc/dev/tutorial/superconductors
the conservation law argument in Builder (e.g. a lead) is
conservation_law=-tau_z
with eigenvalues -1 and 1 yields scattering states of electron and hole type, respectively.
This leads to a block form of the scattering matrix. One can also get the electron and hole projectors as
(projector_e, projector_h) = lead.discrete_symmetry().projectors
In presence of spin (described by sigma matrices) and a magnetic field (giving rise to a Zeeman term) we could
have a conservation law of the following form
conservation_law=np.kron(-tau_z,-sigma_z)
where the Hamiltonian is written in the Nambu basis (e up, e down, h up, -h down). Eigenvalues of this conservation law
are now 1,-1,1,-1, which are degenerate.
Question 1: How can one resolve the four-by-four block structure of the scattering matrix in the electron-hole ⊗ spin up-down space?
Question 2: How can one get the four projectors? I am looking for something like:
(projector_e_up, projector_e_down, projector_h_up, projector_h_down) = lead.discrete_symmetry().projectors