Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction

Details Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction

1996-11-21

arxiv.org/abs/cond-mat/9611162v3

Chaos, Solitons & Fractals 8, 1249 (1997)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1016/S0960-0779(97)00018-0

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.

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