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 τerg, which itself is much smaller than the mean dwell time τdwell. The excitation spectrum of the Josephson junction has a gap Egap, which can be less than the gap ∆ in the bulk superconductors. The average supercurrent is computed in the ergodic regime τerg ≪ h̄/∆, using random-matrix theory, and in the non-ergodic regime τerg ≫ h̄/∆, 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 Egap and ∆ 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 h̄/τerg greater than Egap ≃ h̄/τdwell. 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. To appear in: Chaos, Solitons & Fractals (Pergamon/Elsevier; special issue on Chaos and Quantum Transport in Mesoscopic Cosmos) PACS numbers: 74.50.+r, 74.80.Fp, 05.45.+b Typeset using REVTEX 1