Superfluid stiffness renormalization and critical temperature enhancement in a composite superconductor

Abstract

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, ${t}_{\ensuremath{\perp}}$, 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 ${t}_{\ensuremath{\perp}}$, 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.