Chiral Josephson effect in double layers: The role of particle–hole duality

Abstract

The Josephson effect of inter‐layer s‐wave pairing in a double layer of two chiral metals with Josephson junctions along the direction is considered. Starting from the Bogoliubov de Gennes equations of electron–electron and electron–hole double layers, we employ the duality transformation between the two systems to determine the relation of the zero‐energy quasiparticle modes at a Josephson junction in both systems. The appearance of an exceptional point at zero energy is observed, where the four‐dimensional eigenspace coalesces to a two‐dimensional eigenspace. In the second part of the article, the coupling of the quasiparticle currents and the supercurrent is studied. The coupling is based on the quasiparticle charge conservation in the form of a continuity equation. Although the quasiparticle modes differ between the electron–electron and the electron–hole double layers, their corresponding currents are the same.