Interacting topological insulators: a review

TL;DR

This review explores the intersection of topological insulators and electron-electron interactions, highlighting new phases and phenomena arising from their interplay, including correlated topological states and exotic quantum phases.

Contribution

It provides a comprehensive overview of how topological bandstructures interact with strong correlations, covering stability, new phases, and the relation to quantum magnetism.

Findings

Interaction-induced topological phases like topological Kondo insulators.

Existence of exotic states such as topological Mott insulators and fractional Chern insulators.

Connections between topological bandstructures and frustrated quantum magnetism.

Abstract

The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful research areas for both experimentalists and theorists. The physics of topological insulators is typically well described by band theory and systems of non-interacting fermions. In contrast, several of the most fascinating effects in condensed matter physics merely exist due to electron-electron interactions, examples include unconventional superconductivity, the Kondo effect, and the Mott-Hubbard transition. The aim of this review article is to give an overview of the manifold directions which emerge when topological bandstructures and correlation physics interfere and compete. These include the study of the stability of topological bandstructures and correlated topological insulators. Interaction-induced topological phases such as the topological Kondo insulator provide another exciting topic. More exotic states of matter such as topological Mott insulator and fractional Chern insulators only exist due to the interplay of topology and strong interactions and do not have any bandstructure analogue. Eventually the relation between topological bandstructures and frustrated quantum magnetism in certain transition metal oxides is emphasized.