Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction

TL;DR

This paper investigates how nonlocal Cooper pairs and singlet-triplet transitions influence the critical current in a double quantum dot Josephson junction, revealing signatures consistent with recent experiments and identifying tunable phase transitions.

Contribution

It provides analytical and numerical analysis of nonlocal Cooper pair transport and singlet-triplet transitions in a double quantum dot Josephson junction, including exact on-site interactions.

Findings

Signatures of nonlocal spin-entangled pairs in critical current.

Observation of a tunable singlet-triplet phase transition.

Identification of new signatures of nonlocal Cooper pair transport.

Abstract

We study the critical Josephson current flowing through a double quantum dot weakly coupled to two superconducting leads. We use analytical as well as numerical methods to investigate this setup in the limit of small and large bandwidth leads in all possible charging states, where we account for on-site interactions exactly. Our results provide clear signatures of nonlocal spin-entangled pairs, which support interpretations of recent experiments [Deacon, R. S. et al., Nat. Commun. 6, 7446 (2015)]. In addition, we find that the ground state with one electron on each quantum dot can undergo a tunable singlet-triplet phase transition in the regime where the superconducting gap in the leads is not too large, which gives rise to an additional new signature of nonlocal Cooper pair transport.