Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions

TL;DR

This paper reveals a hidden symmetry in multi-terminal Josephson junctions with quantum dots, enabling simplified analysis and uncovering phenomena like energy band crossings and superconducting transistor effects.

Contribution

It uncovers a hidden symmetry that maps complex multi-terminal junctions to simpler two-terminal models, facilitating analysis across interaction strengths.

Findings

Existence of finite energy band crossings

Superconducting transistor and diode effects

Current phase relation modulation

Abstract

We study a multi-terminal Josephson junction based on an interacting quantum dot coupled to $n$ superconducting BCS leads. Using an Anderson type model of a local level with an arbitrary onsite Coulomb repulsion, we uncover its surprising equivalence with an effective two-terminal junction with symmetric couplings to appropriately phase-biased leads. Regardless of the strength of the Coulomb interaction, this hidden symmetry enables us to apply well-established numerical and theoretical tools for exact evaluation of various physical quantities, and imposes strict relations among them. Focusing on three-terminal devices, we then demonstrate several phenomena such as the existence of the finite energy band crossings, superconducting transistor and diode effects, as well as current phase relation modulation.