Composite fermions description of fractional topological insulators

TL;DR

This paper introduces a new classification scheme for Abelian time-reversal fractional topological insulators using the composite fermions approach, revealing a hierarchy of topological phases with specific spin Hall conductance properties.

Contribution

It applies the composite fermions method to time-reversal symmetric systems, establishing a $ ext{Z}_2$ classification and identifying conditions for stable edge states.

Findings

Hierarchy of topological insulators with quantized spin Hall conductance

Stable edge states occur only for odd p values

New $ ext{Z}_2$ classification scheme for fractional topological insulators

Abstract

We propose a $\mathbb{Z}_{2}$ classification of Abelian time-reversal fractional topological insulators in terms of the composite fermions picture. We consider the standard toy model where spin up and down electrons are subjected to opposite magnetic fields and only electrons of the same spin interact via a repulsive force. By applying the composite fermions approach to this time-reversal symmetric system, we are able to obtain a hierarchy of topological insulators with spin Hall conductance $\sigma_{s}=\frac{e}{2\pi}\frac{p}{2mp+1} $, being $p,m \in\mathbb{N}$. They show stable edge states only for odd $p$, as a direct consequence of the Kramer's theorem.