A route to high temperature superconductivity in composite systems

Apparently, some form of local superconducting pairing persists to temperatures well above the maximum observed $T_c$ in underdoped cuprates, \textit{i.e.} $T_c$ is suppressed due to the small phase stiffness. With this in mind, we consider the following question -- Given a system with a high pairing scale $\Delta_0 $ but with $T_c$ reduced by phase fluctuations, can one design a composite system in which $T_c$ approaches its mean-field value, $T_c\to T_{MF}\approx \Delta_0/2\$? Here, we study a simple two component model in which a "metallic layer" with $\Delta_0=0$ is coupled by single-particle tunneling to a "pairing layer" with $\Delta_0 >0 $ but zero phase stiffness. We show that in the limit that the bandwidth of the metal is much larger than $\Delta_0$, $T_c$ of the composite system can reach the upper limit $T_c \approx\Delta_0/2$.