  Charged excitons (trions) are essential for the optical spectra in low
dimensional doped monolayers (ML) of transitional metal dichalcogenides (TMDC).
Using a direct diagonalization of the three-body Hamiltonian, we explore the
low-lying trion states in four types of TMDC MLs. We show that the trions fine
structure results from the interplay between the spin-valley fine structure of
the single-particle bands and the exchange interaction between the composing
particles. We demonstrate that by variations of the doping and dielectric
environment, trion energy fine structure can be tuned, leading to anti-crossing
of the bright and dark states with substantial implications for the optical
spectra of TMDC MLs.
