Distinct topological excitonic insulators characterized by quantum geometry

TL;DR

This paper explores how quantum geometry influences exotic topological excitonic insulators, revealing phases with unique properties unrelated to topology but driven by geometric wave function distinctions.

Contribution

It introduces a new perspective on excitonic insulators by emphasizing quantum geometry's role, beyond traditional topological classifications, and proposes Floquet engineering to realize these phases.

Findings

Different excitonic phases exhibit identical Chern numbers but distinct spin textures.

Quantum geometry determines physical properties like Kerr responses in excitonic insulators.

Floquet engineering can induce and control these topological excitonic phases in nonequilibrium states.

Abstract

Theintertwining of electron-hole correlation and nontrivial topology is known to give rise to exotic topological excitonic insulators. Here, we show that the involvement of quantum geometry can characterize more exotic excitonic phases exhibiting physical properties that are not influenced by their topology but by geometry. Starting from a topological band insulator and gradually reducing the band gap, many-body interaction can initially generate a p + ip-wave and then an s-wave excitonic insulator. Interestingly, they bear the same Chern number but exhibit completely different spin textures and magneto-optical Kerr responses, reflecting the intricate geometric distinctions in their wave functions. We also propose to enhance the correlation effect via Floquet engineering, which provides a systematic way to realize these topological excitonic insulators and their phase transitions in the nonequilibrium steady states. Our results demonstrate correlated phenomena characterized by quantum geometry, beyond the conventional topological classifications.