Superfluid stiffness renormalization and critical temperature enhancement in a composite superconductor

We study a model of a composite system constructed from a "pairing layer" of disconnected attractive-U Hubbard sites that is coupled by single-particle tunneling, t, to a disordered metallic layer. For small interlayer tunneling the system is described by an effective long-range XY phase model whose critical temperature, T _c, is essentially insensitive to the disorder and is exponentially suppressed by quantum fluctuations. T _c reaches a maximum for intermediate values of t, which we calculate using a combination of mean-field, classical, and quantum Monte Carlo methods. The maximal T _c scales as a fraction of the zero-temperature gap of the attractive sites when U is smaller than the metallic bandwidth, and is bounded by the maximal T _c of the two-dimensional attractive Hubbard model for large U. Our results indicate that a thin, rather than a thick, metallic coating is better suited for the enhancement of T _c at the surface of a phase fluctuating superconductor.