Higher angular momentum band inversions in two dimensions

TL;DR

This paper explores higher angular momentum band inversions in 2D topological phases, introducing models, analyzing interactions, and proposing new topological insulator states protected by rotation symmetry.

Contribution

It introduces minimal lattice models for higher angular momentum band inversions and analyzes their interaction-driven phases and potential for realizing correlated topological states.

Findings

Higher angular momentum band inversions separate trivial and Chern insulators.

Interactions can lead to excitonic insulator phases breaking rotational symmetry.

Ground states of higher Chern number phases resemble multicomponent quantum Hall states.

Abstract

We study a special class of topological phase transitions in two dimensions described by the inversion of bands with relative angular momentum higher than 1. A band inversion of this kind, which is protected by rotation symmetry, separates the trivial insulator from a Chern insulating phase with higher Chern number, and thus generalizes the quantum Hall transition described by a Dirac fermion. Higher angular momentum band inversions are of special interest, as the non-vanishing density of states at the transition can give rise to interesting many-body effects. Here we introduce a series of minimal lattice models which realize higher angular momentum band inversions. We then consider the effect of interactions, focusing on the possibility of electron-hole exciton condensation, which breaks rotational symmetry. An analysis of the excitonic insulator mean field theory further reveals that the ground state of the Chern insulating phase with higher Chern number has the structure of a multicomponent integer quantum Hall state. We conclude by generalizing the notion of higher angular momentum band inversions to the class time-reversal invariant systems, following the scheme of Bernevig-Hughes-Zhang (BHZ). Such band inversions can be viewed as transitions to a topological insulator protected by rotation and inversion symmetry, and provide a promising venue for realizing correlated topological phases such as fractional topological insulators.