# Exploration of the bright and dark exciton landscape and fine structure of MoS$_2$ (using G$_0$W$_0$-BSE)

## TL;DR

This paper investigates the exciton landscape of MoS₂ monolayers, including dark and bright excitons, using advanced GW-BSE calculations, revealing the energetic ordering, binding energies, and orbital origins of excitons relevant for optoelectronic applications.

## Contribution

It provides detailed insights into dark exciton energies and binding energies in MoS₂ using G₀W₀-BSE, including the identification of indirect lowest-energy excitons and scaling rules.

## Key findings

- Lowest-energy exciton is indirect at K'→K
- Dark exciton binding energies scale with quasiparticle energies as 0.25
- Differences in binding energies explained by orbital theory

## Abstract

Spectral ordering between dark and bright excitons in transition metal dichalcogenides is of increasing interest for optoelectronic applications. However, little is known about dark exciton energies and their binding energies. We report the exciton landscape including momentum-forbidden dark excitons of MoS$_{2}$ monolayer using single shot GW-Bethe Salpeter equation (G$_{0}$W$_{0}$-BSE) calculations. We find the lowest-energy exciton to be indirect at ($\textrm K'_{v} \rightarrow \textrm K_{c}$) in agreement with recent GdW-BSE calculations [2D Mater. 6, 035003 (2019)]. We also find that by large, dark exciton binding energies ($E_b$) scale with the quasiparticle energies ($E_g$) according to the $E_b/E_g=0.25$ rule. Differences in exciton binding energies are explained using an orbital theory.