Customizing vortex lattices in strong type-II superconducting nanostructures

We show how to calculate semi-analytically the order parameter in strong type-II superconducting nanostructures where interfaces give rise to spatially non-uniform condensation energies. In particular, we present dense vortex lattice solutions of the order parameter in strips (or thin films), which also incorporate surface superconductivity. We calculate the shear energy between vortex rows parallel to the surfaces and find that it oscillates with the magnetic field. Remarkably, we also find that, at a critical field $H^*$ below $H_{c2}$, the shear energy becomes strictly zero near the surfaces due to the appearance of incommensurate vortex rows.