Non-equilibrium supercurrent through a quantum dot: current harmonics and proximity effect due to a normal metal lead

TL;DR

This paper investigates the behavior of supercurrent and current harmonics in a quantum dot system under non-equilibrium conditions, analyzing the effects of a normal metal lead on the proximity effect and charge transfer mechanisms.

Contribution

It introduces a detailed model of a quantum dot between superconductors with a normal lead, exploring the crossover from coherent to incoherent regimes and the impact on supercurrent.

Findings

Normal probe induces dephasing and reverse proximity effect.

Full crossover from zero to full dephasing characterized.

Supercurrent calculations agree with non-equilibrium current at zero voltage.

Abstract

We consider a Hamiltonian model for a quantum dot which is placed between two superconducting leads with a constant bias imposed between these leads. Using the non-equilibrium Keldysh technique, we focus on the subgap current, where it is known that multiple Andreev reflections (MAR) are responsible for charge transfer through the dot. Attention is put on the DC current and on the first harmonics of the supercurrent. Varying the energy and width of the resonant level on the dot, we first investigate a cross-over from a quantum dot regime to a quantum point contact regime when there is zero coupling to the normal probe. We then study the effect on the supercurrent of the normal probe which is attached to the dot. This normal probe is understood to lead to dephasing, or alternatively to induce reverse proximity effect. We describe the full crossover from zero dephasing to the incoherent case. We also compute the Josephson current in the presence of the normal lead, and find it in excellent agreement with the values of the non-equlibrium current extrapolated at zero voltage.