  We present a theoretical study of photo-absorption in n-doped two-dimensional
(2D) and quasi-2D semiconductors that takes into account the interaction of the
photocreated exciton with Fermi-sea (FS) electrons through (i) Pauli blocking,
(ii) Coulomb screening, and (iii) excitation of FS electron-hole pairs---that
we here restrict to one. The system we tackle is thus made of one exciton plus
zero or one FS electron-hole pair. At low doping, the system ground state is
predominantly made of a "trion-hole"---a trion (two opposite-spin electrons
plus a valence hole) weakly bound to a FS hole---with a small exciton
component. As the trion is poorly coupled to photon, the intensity of the
lowest absorption peak is weak; it increases with doping, thanks to the growing
exciton component, due to a larger coupling between 2-particle and 4-particle
states. Under a further doping increase, the trion-hole complex is less bound
because of Pauli blocking by FS electrons, and its energy increases. The lower
peak then becomes predominantly due to an exciton dressed by FS electron-hole
pairs, that is, an exciton-polaron. As a result, the absorption spectra of
$n$-doped semiconductor quantum wells show two prominent peaks, the nature of
the lowest peak turning from trion-hole to exciton-polaron under a doping
increase. Our work also nails down the physical mechanism behind the increase
with doping of the energy separation between the trion-hole peak and the
exciton-polaron peak, even before the anti-crossing, as experimentally
observed.
