  Just as photons are the quanta of light, plasmons are the quanta of
orchestrated charge-density oscillations in conducting media. Plasmon phenomena
in normal metals, superconductors and doped semiconductors are often driven by
long-wavelength Coulomb interactions. However, in crystals whose Fermi surface
is comprised of disconnected pockets in the Brillouin zone, collective electron
excitations can also attain a shortwave component when electrons transition
between these pockets. Here, we show that the band structure of monolayer
transition-metal dichalcogenides gives rise to an intriguing mechanism through
which shortwave plasmons are paired up with excitons. The coupling elucidates
the origin for the optical side band that is observed repeatedly in monolayers
of WSe$_2$ and WS$_2$ but not understood. The theory makes it clear why
exciton-plasmon coupling has the right conditions to manifest itself distinctly
only in the optical spectra of electron-doped tungsten-based monolayers.
