\textit{Ab initio} \textit{GW}-BSE theory of optical activity in $\alpha$-quartz

TL;DR

This paper develops an ab initio GW-BSE theoretical framework to accurately describe optical activity in solids, specifically applied to $ extalpha$-quartz, emphasizing the importance of excitonic effects.

Contribution

It introduces two formulations for dielectric spatial dispersion within GW-BSE and demonstrates their effectiveness in capturing optical activity in $ extalpha$-quartz.

Findings

Envelope-modulated formulation captures low-frequency optical activity.

Sum-over-exciton-states formulation is crucial for full frequency dependence.

Excitonic many-body effects significantly influence spectral dispersion.

Abstract

We present an ab initio many-body theory of optical activity in solids within the GW-BSE framework. Dielectric spatial dispersion is formulated in two complementary forms: exciton envelope modulation and sum-over-exciton-states expansion. Our application to $\alpha$-quartz reveals that the envelope-modulated formulation captures the low-frequency region, whereas the sum-over-exciton-states formulation is essential to reproduce the correct full frequency dependence. Comparisons with the independent-particle approximation and simple local-field corrections further highlight the decisive role of excitonic many-body effects in shaping the spectral dispersion of optical activity in solids.