Spin-orbit coupled multiband superconductors

Abstract

A model for square lattice spin orbit coupled cooper pairing is derived using mean field theory. We look at three cases, a magnetic field parallel to the lattice, perpendicular to the lattice, and no magnetic field. For the cases of perpendicular or zero field, the cooper pairs have zero momentum, and we are able to find conditions on the spin-basis BCS interaction under which the system produces chiral p-wave cooper pairing, with gaps of the form $\Delta(\bm{k}) \sim k_x + i k_y$. For the parallel field case, we compare calculations with those of \cite{loder} and find corrections to the helicity basis interactions, and thus the gap equations.