Thermodynamics of Non-Hermitian Josephson junctions with exceptional points

TL;DR

This paper develops an analytical thermodynamic framework for non-Hermitian Josephson junctions with exceptional points, revealing universal entropy jumps linked to Majorana zero modes and proposing experimental detection methods.

Contribution

It introduces a formalism for thermodynamics of non-Hermitian systems with EPs and links entropy jumps to Majorana modes, providing analytical boundaries and experimental proposals.

Findings

Entropy shows a universal jump of 1/2 log 2 at EPs.

Supercurrent does not diverge at EPs, contrary to previous claims.

Analytical boundaries for Majorana entropy steps are derived.

Abstract

We present an analytical formulation of the thermodynamics, free energy and entropy, of any generic Bogoliubov de Genes model which develops exceptional point (EP) bifurcations in its complex spectrum when coupled to reservoirs. We apply our formalism to a non-Hermitian Josephson junction where, despite recent claims, the supercurrent does not exhibit any divergences at EPs. The entropy, on the contrary, shows a universal jump of $1/2\log 2$ which can be linked to the emergence of Majorana zero modes (MZMs) at EPs. Our method allows us to obtain precise analytical boundaries for the temperatures at which such Majorana entropy steps appear. We propose a generalized Maxwell relation linking supercurrents and entropy which could pave the way towards the direct experimental observation of such steps in e.g. quantum-dot based minimal Kitaev chains.