Holographic fractional topological insulators in 2+1 and 1+1 dimensions

TL;DR

This paper develops field theory and holographic models for fractional topological insulators in 2+1 and 1+1 dimensions, revealing their topological properties and robustness at strong coupling.

Contribution

It introduces a holographic framework for fractional topological insulators, extending low-energy descriptions to strongly coupled regimes.

Findings

Topological field theories derived from massive Dirac fermions

Holographic realization confirms robustness of topological transport

Potential identification of new states of matter

Abstract

We give field theory descriptions of the time-reversal invariant quantum spin Hall insulator in 2+1 dimensions and the particle-hole symmetric insulator in 1+1 dimensions in terms of massive Dirac fermions. Integrating out the massive fermions we obtain a low-energy description in terms of a topological field theory, which is entirely determined by anomaly considerations. This description allows us to easily construct low-energy effective actions for the corresponding `fractional' topological insulators, potentially corresponding to new states of matter. We give a holographic realization of these fractional states in terms of a probe brane system, verifying that the expected topologically protected transport properties are robust even at strong coupling.