Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures

Abstract

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin ν = 1/3 states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional 6π Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The versatility and efficiency of our setup make it a well suited method to tackle wider questions of edge phases and phase transitions in fractional quantum Hall systems.

Fractional quantum Hall effect: new numerical setup

A numerical setup provides a full microscopic model to describe a fractional quantum Hall system coupled to superconducting leads. The fractional quantum Hall effect is a phenomenon in which the Hall conductance of 2D electrons shows characteristic quantised plateaus. Systems exhibiting this effect can host exotic topological states, some of which have potential for universal quantum computation. However, their experimental investigation is challenging. An international team comprising Cécile Repellin, Ashley Cook, Titus Neupert and Nicolas Regnault demonstrated for the first time a fully microscopic model that allows the quantitative study of such systems, and showed that it identifies the expected key signatures. These results will both enable further numerical work relying on the presented setup and provide guidance for experiments by indicating the parameter regime in which each signature can be observed.