Fractional Chern insulator edges and layer-resolved lattice contacts

TL;DR

This paper proposes a method using layer-resolved lattice contacts to detect genons, non-Abelian topological defects, in fractional Chern insulators, with potential implementation in graphene systems for topological quantum computing.

Contribution

It introduces a novel approach to detect genons in FCIs via momentum differences at edges, enabling experimental identification of non-Abelian defects.

Findings

Layer-resolved lattice contacts can distinguish FCI edge electrons.

Translation symmetry induces quantized momentum differences.

Potential implementation in graphene with artificial lattices.

Abstract

Fractional Chern insulators (FCIs) realized in fractional quantum Hall systems subject to a periodic potential are topological phases of matter for which space group symmetries play an important role. In particular, lattice dislocations in an FCI can host topology-altering non-Abelian topological defects, known as genons. Genons are of particular interest for their potential application to topological quantum computing. In this work, we study FCI edges and how they can be used to detect genons. We find that translation symmetry can impose a quantized momentum difference between the edge electrons of a partially-filled Chern band. We propose {\it layer-resolved lattice contacts}, which utilize this momentum difference to selectively contact a particular FCI edge electron. The relative current between FCI edge electrons can then be used to detect the presence of genons in the bulk FCI. Recent experiments have demonstrated graphene is a viable platform to study FCI physics. We describe how the lattice contacts proposed here could be implemented in graphene subject to an artificial lattice, thereby outlining a path forward for experimental dectection of non-Abelian topological defects.