Superconducting correlations out of repulsive interactions on a fractional quantum Hall edge

Abstract

We consider a fractional quantum Hall bilayer system with an interface between quantum Hall states of filling fractions $(\nu_{\text{top}},\nu_{\text{bottom}})=(1,1)$ and $(1/3,2)$, motivated by a recent approach to engineering artificial edges~\cite{2018NatPh..14..411R}. We show that random tunneling and strong repulsive interactions within one of the layers will drive the system to a stable fixed point with two counterpropagating charge modes which have attractive interactions. As a result, slowly decaying correlations on the edge become predominantly superconducting. We discuss the resulting observable effects, and derive general requirements for electron attraction in Abelian quantum Hall states. The broader interest in fractional quantum Hall edge with quasi-long range superconducting order lies in the prospects of hosting exotic anyonic boundary excitations, that may serve as a platform for topological quantum computation.