Excitonic Effects In The Optical Properties Of 2d Materials: An Equation Of Motion Approach

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 WS2. 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 WS2. We also derive a semi-analytical version of Ellitot's formula for TMDC's.