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

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 superconducting diode effect, as well as current phase relation modulation. Brief analysis of four-terminal devices is also given.