Collective modes in a Dirac insulator with short range interactions

TL;DR

This paper investigates collective excitations in a Haldane model with short-range interactions, revealing topologically distinct modes that can differentiate trivial and Chern insulator phases, with implications for cold atom experiments.

Contribution

It introduces a new analysis of collective modes in a Haldane model with interactions, linking dispersion relations to topological phases and proposing experimental detection methods.

Findings

Collective modes are low energy and lie in the band gap.

Dispersion relations differ between trivial and Chern insulator phases.

Proposed detection of modes in cold atom systems.

Abstract

We study a Haldane model with nearest neighbor interactions. We find one-dimensional like collective modes arising due to the interplay of pseudo-spin and valley degrees of freedom. In the large band gap or moderate interaction limit, these excitations are low energy modes lying in the band gap. The dispersion relations are qualitatively different in trivial insulator phase and Chern insulator phase, thus can be used to identify the topology of the Haldane model with the bulk property. We also discuss how to detect these modes in cold atom systems. An abelian gauge theory will emerge when a physical current-current interaction is introduced to the Haldane model or the Kane-Mele model.