# Excitonic effects in the optical properties of 2D materials: An equation of motion approach

## TL;DR

This paper introduces an efficient equation of motion method to analyze excitonic effects in 2D transition-metal dichalcogenides, accurately capturing binding energies and spectral features with less computational effort.

## Contribution

It presents a unified, less computationally demanding approach to study excitonic properties in TMDC monolayers, incorporating exchange energy effects and providing semi-analytical formulas.

## Key findings

- Accurately models exciton binding energies and spectra in TMDCs.
- Shows the importance of exchange energy at the $b3$-point for spectral accuracy.
- Achieves good agreement with experimental Rydberg series and absorption spectra.

## Abstract

We present a unified description of the excitonic properties of four monolayer transition-metal dichalcogenides (TMDC's) using an equation of motion method for deriving the Bethe-Salpeter equation in momentum space. Our method is able to cope with both continuous and tight-binding Hamiltonians, and is less computational demanding than the traditional first-principles approach. We show that the role of the exchange energy is essential to obtain a good description of the binding energy of the excitons. The exchange energy at the $\Gamma-$point is also essential to obtain the correct position of the C-exciton peak. Using our model we obtain a good agreement between the Rydberg series measured for WS$_2$. We discuss how the absorption and the Rydberg series depend on the doping. Choosing $r_0$ and the doping we obtain a good qualitative agreement between the experimental absorption and our calculations for WS$_2$. We also derive a semi-analytical version of Ellitot's formula for TMDC's.