Two-dimensional superconducting arrays in a magnetic field: Effects of lattice structures

We study the effects of lattice structures on the behavior of two-dimensional ordered superconducting arrays in a transverse magnetic field, using both mean-field approximations and Monte Carlo simulations. The transition temperature $T_c$ and the ground-state energy $E_g$ are found to be periodic in the field with a period one flux quantum per lattice cell while the substructure within one period depends upon the underlying lattice structure: The curves $T_c^{\mathrm{MF}}$ and -$E_g$ show a secondary maximum at f=(1/2) in both square and triangular lattices but at f=(1/3) in honeycomb; furthermore, the triangular array shows a conspicuous cusp at f=(1/4), which is not seen in other lattices but is in apparent agreement with the experiment. (f is the fractional number of flux quanta per lattice cell.) In addition to f=(1/4), a similar double transition is found at f=(3/8) in a triangular lattice. The T=0 critical current densities, T=0 helicity moduli, and the Monte Carlo transition temperatures at a few values of f all show similar characteristics.