Classification and analysis of two dimensional abelian fractional topological insulators

TL;DR

This paper develops a comprehensive theoretical framework for two-dimensional abelian fractional topological insulators, identifying conditions for protected edge modes and unifying previous models within this approach.

Contribution

It introduces a general Chern-Simons theory framework for abelian fractional topological insulators and establishes criteria for protected edge states, unifying prior examples.

Findings

Derived the most general Chern-Simons theories for these insulators.

Established a criterion for protected gapless edge modes.

Unified previous models as special cases within the framework.

Abstract

We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct the most general Chern-Simons theories that can describe these states. We then derive a criterion for when these systems have protected gapless edge modes -- that is, edge modes that cannot be gapped out without breaking time reversal or charge conservation symmetry. The systems with protected edge modes can be regarded as fractionalized analogues of topological insulators. We show that previous examples of 2D fractional topological insulators are special cases of this general construction. As part of our derivation, we define the concept of "local Kramers degeneracy" and prove a local version of Kramers theorem.