Monte Carlo Study of a Periodically Pinned 2D Superconductor

We show that a natural assumption on the moving mechanism of vortices in a periodically pinned, two-dimensional superconductor in the mixed state is the basis for a n-clock-like model. The pinning points are considered to be centered in each unit cell of the superconducting lattice. This property enables one to use a discrete version of the XY model used in the simulations focusing on the melting of the Abrikosov lattice of vortices in a system of Josephson arrays. A Monte Carlo study performed on the corresponding Hamiltonian in a field given by a filling factor of f=1/2 exhibits two phase transitions, at the temperatures T$\text{}_{c1}$≈0.325 and T$\text{}_{m}$≈0.65. The numerical estimation of the Challa parameters for both transitions indicates their continuous nature. The physical meaning of the lower transition is the expulsion of the magnetic field from the superconducting system, i.e. the Meissner effect. The physical equivalent of the upper transition is the melting of the pinned vortex lattice.