Route to high-temperature superconductivity in composite systems

Apparently, some form of local superconducting pairing persists up to temperatures well above the maximum observed $T_c$ in underdoped cuprates; 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, $T_c\to T_{\text{MF}}\approx {\Delta }_0/2$? 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 where the bandwidth of the metal is much larger than ${\Delta }_0$, the $T_c$ of the composite system can reach the upper limit $T_c\approx {\Delta }_0/2$.

Figure 1

(Color online) $T_c$ (◻) and $T_{\text{MF}}$ (◯) obtained from solving Eqs. (6, 7, 8, 9) numerically for $n=1.5$, $t=1$, $U=1$ as a function of $t_{\perp }$. The dashed curves are fits to the data according to Eqs. (13, 15). $A=0.235$ was used in the fit.

Figure 2

(Color online) $T_c\left(\text{max}\right)$ (maximized over $t_{\perp }$) for different values of $U$ and fixed $t=1$, $n=1.5$. $T_c\left(\text{max}\right)$ is shown as a function of ${\Delta }_0\approx U/2$, which is the $T=0$, $t_{\perp }=0$ gap for the same $U$. The dashed line is the mean-field transition temperature for $t_{\perp }=0$, $T_{\text{MF},0}\approx {\Delta }_0/2$. Inset: $t_{\perp }\left(\text{max}\right)$, in which $T_c\left(\text{max}\right)$ is obtained, as a function of ${\Delta }_0$.

Figure 3

(Color online) Same as Fig. 2 for the case of superconducting wires [$t^{\prime }=t$ in Eq. (3)]. $T_c\left(\text{max}\right)/t$ (maximized over $t_{\perp }$) is shown as a function of ${\Delta }_0/t$. The dashed line shows the mean-field transition temperature at $t_{\perp }=0$, $T_{\text{MF},0}/t\approx 2{\Delta }_0/\left(3.5t\right)$. Inset: $t_{\perp }\left(\text{max}\right)/t$ as a function of ${\Delta }_0/t$.