ac Josephson effect in asymmetric superconducting quantum point contacts

TL;DR

This paper studies the ac Josephson effect in asymmetric superconducting quantum point contacts, analyzing how unequal gaps and continuum states influence current-voltage characteristics, especially at low bias and in the ballistic limit.

Contribution

It provides a detailed quasiclassical analysis of the ac Josephson effect in asymmetric contacts, highlighting the roles of bound and continuum states in current behavior.

Findings

Continuum states contribute to current in asymmetric gaps.

Current-voltage characteristics depend on bound and continuum states.

Temperature dependence of dc component follows a hyperbolic tangent law.

Abstract

We investigate ac Josephson effects between two superconductors connected by a single-mode quantum point contact, where the gap amplitudes in the two superconductors are unequal. In these systems, it was found in previous studies on the dc effects that, besides the Andreev bound-states, the continuum states can also contribute to the current. Using the quasiclassical formulation, we calculate the current-voltage characteristics for general transmission $D$ of the point contact. To emphasize bound versus continuum states, we examine in detail the low bias, ballistic (D=1) limit. It is shown that in this limit the current-voltage characteristics can be determined from the current-phase relation, if we pay particular attention to the different behaviors of these states under the bias voltage. For unequal gap configurations, the continuum states give rise to non-zero sine components. We also demonstrate that in this limit the temperature dependence of the dc component follows $\tanh(\Delta_s/2T)$, where $\Delta_s$ is the smaller gap, with the contribution coming entirely from the bound state.