Non-equilibrium cotunneling in interacting Josephson junctions

TL;DR

This paper develops a Liouville space formalism to analyze non-equilibrium transport in interacting superconducting nanojunctions, revealing complex current behaviors, including 0- transitions caused by strong interactions and tunneling.

Contribution

It introduces a novel Liouville space approach to study finite gap effects and cotunneling in interacting Josephson junctions, highlighting the interplay of interactions and tunneling.

Findings

Identification of virtual processes leading to Andreev and Josephson currents

Dependence of current on gate and bias voltage analyzed

Discovery of 0- transitions in critical current

Abstract

We investigate non-equilibrium transport through interacting superconducting nanojunctions using a Liouville space approach. The formalism allows us to study finite gap effects, and to account for both quasiparticle and Cooper pair tunneling. With focus on the weak tunneling limit, we study the stationary dc and ac current up to second order (cotunneling) in the hybridization energy. We identify the characteristic virtual processes that yield the Andreev and Josephson current and obtain the dependence on the gate and bias voltage for the dc current, the critical current and the phase-dependent dissipative current. In particular, the critical current is characterized by regions in the stability diagram in which its sign changes from positive to negative, resulting in a multitude of 0-\pi transitions. The latter signal the interplay between strong interactions and tunneling at finite bias.