Signatures of exceptional points in multi-terminal SNS junctions

Exceptional points are a characteristic feature of open quantum systems, most commonly explored in the context of non-hermitian Hamiltonians. Non-hermitian Hamiltonians can be realized, for example, in superconducting-normal junctions, where couplings to a normal lead induces the non-hermiticity. We study few-level quantum-dot systems connected to superconducting and normal leads. Using transport formalism, we show that the exceptional points are observable through spectroscopy of the Andreev states, but less visible in the current-phase relations. This transport formalism also allows us to address ambiguities about the interpretation of non-hermitian Hamiltonians and to extend the theory beyond the infinite-gap limit. Furthermore, we consider the effect of interactions.