Gauge-invariant optical selection rules for excitons

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.