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

• Main Author: Chaves, A. J.
• Publication Date: 2017
• Other Authors: Ribeiro, R. M., Frederico, T., Peres, N. M. R.
• Format: Article
• Language: eng
• Source: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Download full: https://hdl.handle.net/1822/47442
• topic: Excitons; TMD; Bethe-Salpeter; Dirac; 2D materials; transition metal dichalcogenides; Ciências Naturais::Ciências Físicas; Science & Technology

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.