Nonequilibrium effects in tunnel Josephson junctions

TL;DR

This paper investigates how nonequilibrium quasiparticle dynamics and bound states in voltage-biased tunnel Josephson junctions with long superconducting leads lead to higher harmonics and enhanced dc currents, especially at low voltages.

Contribution

It introduces a detailed analysis of nonequilibrium effects, including Andreev bound states and their impact on current harmonics and dc current, in long diffusive superconducting junctions.

Findings

Formation of oscillating Andreev bound states near the junction.

Generation of higher even harmonics in the Josephson current.

Non-equilibrium dc current can significantly exceed tunnel model predictions.

Abstract

We study nonequilibrium effects in current transport through voltage biased tunnel junction with long diffusive superconducting leads at low applied voltage, $eV \ll 2\Delta$, and finite temperatures. Due to a small value of the Josephson frequency, the quasiparticle spectrum adiabatically follows the time evolution of the superconducting phase difference, which results in the formation of oscillating bound states in the vicinity of the tunnel junction (Andreev band). The quasiparticles trapped by the Andreev band generate higher even harmonics of the Josephson ac current, and also, in the presence of inelastic scattering, a non-equilibrium dc current, which may considerably exceed the dc quasiparticle current given by the tunnel model. The distribution of travelling quasiparticles also deviates from the equilibrium due to the spectrum oscillations, which results in an additional contribution to the dc current, proportional to $\sqrt{V}$.