Higher angular momentum band inversions in two dimensions

This talk discusses 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. We introduce a series of minimal lattice models which realize higher angular momentum band inversions. Interaction effects are considered, focusing on the possibility of electron-hole exciton condensation, which breaks rotational symmetry. We further describe how the notion of higher angular momentum band inversions can be generalized to time-reversal invariant systems. 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.