Topological Insulators and Quantum Spin Liquids

TL;DR

This paper reviews recent connections between topological insulators and quantum spin liquids, emphasizing the role of the quantum Hall effect, interactions, and material candidates like oxides with heavy transition metals.

Contribution

It provides a comprehensive overview of the relationships between topological insulators and quantum spin liquids in various dimensions, highlighting new theoretical insights and potential experimental platforms.

Findings

Quantum Hall effect links topological insulators and chiral spin liquids.

Interactions in topological insulators can lead to novel phases.

Heavy transition metal oxides are promising for discovering new topological phenomena.

Abstract

In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect plays a key role in relating topological insulators and chiral spin liquids described by fermionic excitations, and we describe a procedure for "generating" a certain class of topological states. In three dimensions we discuss interesting relationships between certain quantum spin liquids and interacting "exotic" variants of topological insulators. We focus attention on better understanding interactions in topological insulators, and the phases nearby in parameter space that might result from moderate to strong interactions in the presence of strong spin-orbit coupling. We stress that oxides with heavy transition metal ions, which often host a competition between electron interactions and spin-orbit coupling, are an excellent place to search for unusual topological phenomena and other unconventional phases.