Abstract
The effect of a periodic pinning array on the vortex state in a two-dimensional superconductor at low temperatures is studied within the framework of the Ginzburg-Landau approach. It is shown that an 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 orbital description, we derive a rather detailed picture of the low-temperature vortex-state phase diagram for the first matching magnetic field. 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.
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