Enhancing $T_{\mathrm{c}}$ in a composite superconductor/metal bilayer system: a dynamical cluster approximation study

TL;DR

This study uses the dynamical cluster approximation to investigate how coupling an attractive Hubbard layer to a metallic layer affects the superconducting transition temperature, revealing a nonmonotonic relationship influenced by hybridization strength.

Contribution

It provides a detailed analysis of the effects of metal coupling on $T_c$ in an intermediate coupling Hubbard system, highlighting the nonmonotonic behavior and underlying competition mechanisms.

Findings

Superconducting $T_c$ shows nonmonotonic dependence on hybridization strength.

Coupling reduces the effective pairing interaction, limiting $T_c$ enhancement.

Maximum $T_c$ achieved is below that of the isolated negative-$U$ Hubbard model.

Abstract

It has been proposed that the superconducting transition temperature $T_{\mathrm{c}}$ 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 $T_{\mathrm{c}}$ exhibits a nonmonotonic dependence on the strength of the hybridization $t_{\perp}$. This behavior arises from a reduction of the effective pairing interaction in the correlated layer that out-competes the growth in the intrinsic pair-field susceptibility induced by the coupling to the metallic layer. We find that the largest $T_{\mathrm{c}}$ inferred here for the composite system is below the maximum value currently estimated for the isolated negative-$U$ Hubbard model.