Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction

P. W. Brouwer; C. W. J. Beenakker

doi:10.1016/S0960-0779(97)00018-0

paper

Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction

arXiv:cond-mat/9611162 · doi:10.1016/S0960-0779(97)00018-0

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 $τ_{er g}$ , which itself is much smaller than the mean dwell time $τ_{d w e l l}$ . The excitation spectrum of the Josephson junction has a gap $E_{g a p}$ , which can be less than the gap $Δ$ in the bulk superconductors. The average supercurrent is computed in the ergodic regime $τ_{er g} ≪ ℏ/Δ$ , using random-matrix theory, and in the non-ergodic regime $τ_{er g} ≫ ℏ/Δ$ , 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 $E_{g a p}$ and $Δ$ 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 $ℏ/ τ_{er g}$ greater than $E_{g a p} ≃ ℏ/ τ_{d w e l l}$ . 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.

14 pages with 2 figures; the revision corrects the published version in Eqs. 8, 15, and 21d (with thanks to Marlies Goorden)

Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction

Abstract

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