  Strong Coulomb interaction in atomically-thin transition metal
dichalcogenides makes these systems particularly promising for studies of
excitonic physics. Of special interest are the manifestations of the charged
excitons, also known as trions, in the optical properties of two-dimensional
semiconductors. In order to describe the optical response of such a system, the
exciton interaction with resident electrons should be explicitly taken into
account. In this paper we demonstrate that this can be done both in the trion
(essentially, few-particle) and Fermi-polaron (many-body) approaches, which
produce equivalent results provided that the electron density is sufficiently
low and the trion binding energy is much smaller than the exciton one. Here we
consider the oscillator strengths of the optical transitions related to the
charged excitons, fine structure of trions and Zeeman effect, as well as
photoluminescence of trions illustrating the applicability of both
few-particles and many-body models.
