Vortex states in 2D superconductor at high magnetic field in a periodic pinning potential

The effect of a periodic pinning array on the vortex state in a 2D superconductor at low temperatures is studied within the framework of the Ginzburg-Landau approach. It is shown that attractive interaction of vortex cores to a commensurate pin lattice stabilizes vortex solid phases with long range positional order against violent shear fluctuations. Exploiting a simple analytical method, based on the Landau orbitals description, we derive a rather detailed picture of the low temperatures vortex state phase diagram. It is predicted that for sufficiently clean samples application of an artificial periodic pinning array would enable one to directly detect the intrinsic shear stiffness anisotropy characterizing the ideal vortex lattice.