Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction

Abstract

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 τ erg, which itself is much smaller than the mean dwell time τ dwell. The excitation spectrum of the Josephson junction has a gap E gap, which can be less than the gap Δ in the bulk superconductors. The average supercurrent is computed in the ergodic regime τ erg ⪡ h ̵ Δ , using random-matrix theory, and in the non-ergodic regime τ erg ⪢ h ̵ Δ , 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 A 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 h ̵ τ erg greater than E gap ∼- h ̵ τ 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.