Beyond Band Insulators: Topology of Semi-metals and Interacting Phases

TL;DR

This paper reviews recent advances in understanding topological phases in gapless and interacting systems, highlighting Weyl semimetals and interaction-stabilized edge states beyond traditional insulators.

Contribution

It provides a comprehensive overview of topological phenomena in semi-metals and interacting phases, extending the theory beyond non-interacting gapped systems.

Findings

Identification of stable topological properties in gapless systems like Weyl semimetals

Progress in describing topological phases with interactions and symmetry

Discovery of new edge states stabilized by interactions and symmetry

Abstract

The theory of topological insulators and superconductors has mostly focused on non-interacting and gapped systems. This review article discusses topological phases that are either gapless or interacting. We discuss recent progress in identifying gapless systems with stable topological properties (such as novel surface states), using Weyl semimetals as an illustration. We then review recent progress in describing topological phases of interacting gapped systems. We explain how new types of edge states can be stabilized by interactions and symmetry, even though the bulk has only conventional excitations and no topological order of the kind associated with Fractional Quantum Hall states.