Mesoscopic p-wave superconductor near the phase transition temperature

We study the finite-size and boundary effects on a p-wave superconductor in a mesoscopic rectangular sample using Ginzburg-Landau (GL) and quasi-classical (QC) Green's function theory. Except for a square sample with parameters far away from the isotropic weak-coupling limit, the ground state near the critical temperature always prefers a time-reversal symmetric state, where the order parameter can be represented by a real vector. For large aspect ratio, this vector is parallel to the long side of the rectangle. Within a critical aspect ratio, it has instead a vortex-like structure, vanishing at the sample center.