Perspective on trions and excitons in two-dimensional atomically thin materials

Charged excitons or trions are essential for optical spectra in low-dimensional doped monolayers of transitional metal dichalcogenides. This Perspective aims to provide an overview of theoretical approaches that can be employed to predict optical spectra, including many-body interactions leading to tightly bound excitons and trions. The approaches include solutions of the Bethe-Salpeter equation for excitons and the Tamm-Dancoff equation for trions. The resulting energy spectra and two-body exciton wavefunctions and three-body trion wavefunctions allow calculations of transition matrix elements for optical spectra in transition-metal dichalcogenide monolayers as a function of doping, temperature, dielectric environment, and in the presence of an optical cavity. The external control by doping and dielectric environment allows tuning of the fine structure of the trion and exciton energies, leading to the anticrossing of the bright and dark states, enabling expanded or superior optical device functionality.