Gauge-invariant optical selection rules for excitons

TL;DR

This paper develops a gauge-invariant formulation of optical selection rules for excitons, enhancing the theoretical framework for understanding excitonic states in quantum materials, especially 2D semiconductors.

Contribution

It introduces a chiral formulation of the gauge-invariant interband index, making optical selection rules for excitons gauge-invariant and more robust for topological classification.

Findings

Introduces a gauge-invariant, chiral interband index.

Provides gauge-invariant optical selection rules for excitons.

Strengthens the theoretical understanding of excitons in quantum materials.

Abstract

Presently, the optical selection rules for excitons under circularly-polarized light are manifestly gauge-dependent. Recently, Fernando et al. introduced a gauge-invariant, quantized interband index. This index may improve the topological classification of material excited states because it is intrinsically an inter-level quantity. In this work, we expand on this index to introduce its chiral formulation, and use it to make the selection rules gauge-invariant. We anticipate this development to strengthen the theory of quantum materials, especially two-dimensional semiconductor photophysics.