Fractional Topological Insulators -- a Pedagogical Review

TL;DR

This review introduces fractional topological insulators, exploring their theoretical foundations, properties, and stability of edge modes in two, three, and intermediate dimensions, highlighting recent advances and open questions.

Contribution

It provides a comprehensive pedagogical overview of fractional topological insulators, including new insights into their surface states and stability in various dimensions.

Findings

Fractional topological insulators support fractionally charged excitations.

Edge modes in these systems are robust against perturbations.

Surface states in 3D systems exhibit unique stability properties.

Abstract

Fractional topological insulators are electronic systems that carry fractionally charged excitations, conserve charge and are symmetric to reversal of time. In this review we introduce the basic essential concepts of the field, and then survey theoretical understanding of fractional topological insulators in two and three dimensions. In between, we discuss the case of "two and a half dimensions", the fractional topological insulators that may form on the two dimensional surface of an unfractionalized three dimensional topological insulator. We focus on electronic systems and emphasize properties of edges and surfaces, most notably the stability of gapless edge modes to perturbations.