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_perp, to a disordered metallic layer. For small inter-layer 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_perp, 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.