Chiral Josephson effect in double layers: the role of particle-hole duality

TL;DR

This paper explores the Josephson effect in double-layer chiral metals, focusing on how particle-hole duality influences zero-energy modes and supercurrent coupling, revealing different zero-energy mode behaviors despite similar current distributions.

Contribution

It introduces the role of particle-hole duality in the Josephson effect of double-layer chiral metals and analyzes zero-energy modes and supercurrent interactions.

Findings

Duality relation affects zero-energy mode degeneracy.

Same current distribution in electron-electron and electron-hole systems.

Different zero-energy modes arise despite similar currents.

Abstract

The Josephson effect of inter-layer s-wave pairing in a double layer of two chiral metals is considered. We employ the duality relation between electron-electron and electron-hole double layers to discuss the zero-energy eigenmodes at a domain wall and their coupling to the superfluid state. This is described in terms of the quasiparticle current and the supercurrent. It turns out that the degeneracy of the zero-energy eigenmodes is resolved by the coupling to the supercurrent. The duality relation between the electron-electron and electron-hole double layers leads to the same current distribution in both systems but to different zero-energy modes.