Giant Proximity Effect in a Phase-Fluctuating Superconductor

When a tunneling barrier between two superconductors is formed by a normal material that would be a superconductor in the absence of phase fluctuations, the resulting Josephson effect can undergo an enormous enhancement. We establish this novel proximity effect by a general argument as well as a numerical simulation and argue that it may underlie recent experimental observations of the giant proximity effect between two cuprate superconductors separated by a barrier made of the same material rendered normal by severe underdoping.

Figure 1

Superconducting phase distribution in the $J-J^{\prime }-J$ junction with $J^{\prime }/J=0.3$ and a vortex-antivortex pair with size (a) $r=0.3d$ and (b) $r=d$. (c) Energy of the vortex-antivortex pair, Eq. (4), in units of $J$ as a function of the pair size in units of $d$, for $J^{\prime }/J=0.2$. (d) Disk geometry used to estimate the vortex unbinding temperature.

Figure 2

Helicity modulus as a function of temperature of the (a) 2D system with $L=128$ and (b) the 3D system with $L=32$ and different sizes of the barrier $d$ with $J^{\prime }/J=0.4$.

Figure 3

(a) Junction critical temperature $T_{\mathrm{eff}}$ as a function of $x=\ln d/\ln L$ for three different ratios $J^{\prime }/J=0.7$, 0.4 and 0.1 in two dimensions. Finite size effects prevent these points from falling exactly on a smooth curve. The arrows indicate the expected $T_c^{\prime }$ values, reached when $d\to L$. Both $d$ and $L$ are measured in units of $\xi$. (b) Comparison between the $SPS$ model and the conventional $SNS$ proximity effect.