Charge $2e/3$ superconductivity and topological degeneracies without localized zero modes in bilayer fractional quantum Hall states

Understand

It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states.

• Here we propose an alternate route to creating, manipulating, and measuring topologically protected degeneracies in bilayer FQH states coupled to superconductors, without the creation of localized parafermion zero modes.
• We focus mainly on electron-hole bilayers, with a $\pm 1/3$ Laughlin FQH state in each layer, with boundaries that are proximity-coupled to a superconductor.
• We show that the superconductor induces charge $2e/3$ quasiparticle-pair condensation at each boundary of the FQH state, and that this leads to (1) topologically protected degeneracies that can be measured through charge sensing experiments and (2) a fractional charge $2e/3$ AC Josephson effect.