Enhancing Tc in a composite superconductor/metal bilayer system: A dynamical cluster approximation study

It has been proposed that the superconducting transition temperature ${T}_{\text{c}}$ of an unconventional superconductor with a large pairing scale but strong phase fluctuations can be enhanced by coupling it to a metal. However, the general efficacy of this approach across different parameter regimes remains an open question. Using the dynamical cluster approximation, we study this question in a system composed of an attractive Hubbard layer in the intermediate coupling regime, where the magnitude of the attractive Coulomb interaction $|U|$ is slightly larger than the bandwidth $W$, hybridized with a noninteracting metallic layer. We find that while the superconducting transition becomes more mean-field-like with increasing interlayer hopping, the superconducting transition temperature ${T}_{\text{c}}$ exhibits a nonmonotonic dependence on the strength of the hybridization ${t}_{\ensuremath{\perp}}$. This behavior arises from a reduction of the effective pairing interaction in the correlated layer that outcompetes the growth in the intrinsic pair-field susceptibility induced by the coupling to the metallic layer. We find that the largest ${T}_{\text{c}}$ inferred here for the composite system is comparable to the maximum value currently estimated for the isolated negative-$U$ Hubbard model.