Wannier-function approach to phase transitions in superconducting films

Abstract

We describe a method for treating fluctuations in two-dimensional superconducting films in zero magnetic field. The method involves expanding the order parameter ψ(x,y) in empty-lattice Wannier functions of a fictitious square lattice. Despite the discrete basis, the order parameter is continuous and has no unphysical pinning. The thermodynamics of the model is a function of a single variable analogous to the Josephson coupling in granular superconductors. We estimate the Kosterlitz-Thouless (KT) transition temperature Tc 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, Tc is further reduced, the Coulomb-gas scaling hypothesis of Minnhagen is automatically satisfied, and the jump in superfluid density at the transition may possibly be nonuniversal. Snapshots of ψ(x,y) near Tc reveal the rapid development of pairs of oppositely charged vortices, accompanied by zeros of the order parameter, and, above Tc, by unpaired vortices, in agreement with the original KT picture. The extension of this approach to layered three-dimensional superconductors is briefly discussed.

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