WANNIER-FUNCTION APPROACH TO PHASE-TRANSITIONS IN SUPERCONDUCTING FILMS

We describe a method for treating fluctuations in two-dimensional supe rconducting films in zero magnetic field. The method involves expandin g the order parameter psi(x,y) in empty-lattice Wannier functions of a fictitious square lattice. Despite the discrete basis, the order para meter is continuous and has no unphysical pinning. The thermodynamics of the model is a function of a single variable analogous to the Josep hson coupling in granular superconductors. We estimate the Kosterlitz- Thouless (KT) transition temperature T(c) of the model by Monte Carlo techniques. If amplitude fluctuations are neglected, the model reduces to a partially frustrated XY Hamiltonian, even in zero magnetic field . With amplitude fluctuations, T(c) is further reduced, the Coulomb-ga s scaling hypothesis of Minnhagen is automatically satisfied, and the jump in superfluid density at the transition may possibly be nonuniver sal. Snapshots of psi(x,y) near T(c) reveal the rapid development of p airs of oppositely charged vortices, accompanied by zeros of the order parameter, and, above T(c), by unpaired vortices, in agreement with t he original KT picture. The extension of this approach to layered thre e-dimensional superconductors is briefly discussed.