Square vortex lattice in p-wave superconductors

Abstract
Making use of the Ginzburg Landau equation for isotropic p-wave superconductors, we construct the single vortex solution in part analytically. The fourfold symmetry breaking term arising from the tetragonal symmetry distortion of the Fermi surface is crucial, since this term indicates a fourfold distortion of the vortex core somewhat similar to the one found in d-wave superconductors. This fourfold distortion of the vortex core in turn favors the square vortex lattice as observed recently by small angle neutron scattering (SANS) experiment from Sr₂RuO₄. We find that the hexagonal vortex lattice at H = H_c1 transforms into the square one for H = H_cr = 0.26-H_c2. On the other hand the SANS data does not reveal such transition. The square vortex covers everywhere studied by the SANS implying H_cr is very close to H_c1. Therefore some improvement in the present model is certainly desirable.