Effect of fermion indistinguishability on optical absorption of doped two-dimensional semiconductors

We study the optical absorption spectrum of a doped two-dimensional semiconductor in the spin-valley polarized limit. In this configuration, the carriers in the Fermi sea are indistinguishable from one of the two carriers forming the exciton. Most notably, this indistinguishability requires the three-body trion state to have p-wave symmetry. To explore the consequences of this, we evaluate the system's optical properties within a polaron description, which can interpolate from the low-density limit, where the relevant excitations are few-body bound states, to higher-density many-body states. In the parameter regime where the trion is bound, we demonstrate that the spectrum is characterized by an attractive quasiparticle branch, a repulsive branch, and a many-body continuum, and we evaluate the doping dependence of the corresponding energies and spectral weights. In particular, at low doping we find that the oscillator strength of the attractive branch scales with the square of the Fermi energy as a result of the trion's p-wave symmetry. Upon increasing density, we find that the orbital character of the states associated with these branches interchanges. We compare our results with previous investigations of the scenario where the Fermi sea involves carriers distinguishable from those in the exciton, for which the trion ground state is s wave.