Driven Andreev molecule

TL;DR

This paper investigates the non-equilibrium properties of a three-terminal Josephson junction with quantum dots, revealing how Floquet resonances influence Andreev bound states, MAR steps, and interference effects in the I-V characteristics.

Contribution

It introduces a Floquet-based approach to analyze the driven Andreev molecule, providing numerical spectra and insights into non-equilibrium resonances and interference phenomena.

Findings

Floquet resonances shape MAR steps in I-V curves

Proximity causes splitting of MAR steps

Interference effects induce oscillations at large distances

Abstract

We study the three terminal S-QD-S-QD-S Josephson junction biased with commensurate voltages. In the absence of an applied voltage, the Andreev bound states on each quantum dot hybridize forming an `Andreev molecule'. However, understanding of this system in a non-equilibrium setup is lacking. Applying a dc voltage on the bijunction makes the system time-periodic, and the equilibrium Andreev bound states evolve into a ladder of resonances with a finite lifetime due to multiple Andreev reflections (MAR). Starting from the time-periodic Bogoliubov-de Gennes equations we map the problem to a tight-binding chain in the (infinite) Floquet space. The resolvent of this non-Hermitian block matrix is obtained via a continued fraction method. We numerically calculate the Floquet-Andreev spectra which could be probed by local tunneling spectroscopy on the dots. We also consider the subgap current, and show that the Floquet resonances determine the position of the MAR steps. Proximity of the two dots causes splitting of the steps, while at large distances we observe interference effects which cause oscillations in the I-V curves. The latter effect should persist at very long distances.