Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction

We calculate the supercurrent through a Josephson junction consisting of a phase-coherent metal particle (quantum dot), weakly coupled to two superconductors. The classical motion in the quantum dot is assumed to be chaotic on time scales greater than the ergodic time $\tau_{erg}$, which itself is much smaller than the mean dwell time $\tau_{dwell}$. The excitation spectrum of the Josephson junction has a gap $E_{gap}$, which can be less than the gap $\Delta$ in the bulk superconductors. The average supercurrent is computed in the ergodic regime $\tau_{erg} \ll \hbar/\Delta$, using random-matrix theory, and in the non-ergodic regime $\tau_{erg} \gg \hbar/\Delta$, using a semiclassical relation between the supercurrent and dwell-time distribution. In contrast to conventional Josephson junctions, raising the temperature above the excitation gap does not necessarily lead to an exponential suppression of the supercurrent. Instead, we find a temperature regime between $E_{gap}$ and $\Delta$ where the supercurrent decreases logarithmically with temperature. This anomalously weak temperature dependence is caused by long-range correlations in the excitation spectrum, which extend over an energy range $\hbar/\tau_{erg}$ greater than $E_{gap} \simeq \hbar/\tau_{dwell}$. A similar logarithmic temperature dependence of the supercurrent was discovered by Aslamazov, Larkin, and Ovchinnikov, in a Josephson junction consisting of a disordered metal between two tunnel barriers.