  Atomically thin layers of transition metal dichalcogenides (TMDCs) exhibit
exceptionally strong Coulomb interaction between charge carriers due to the
two-dimensional carrier confinement in connection with weak dielectric
screening. The van der Waals nature of interlayer coupling makes it easy to
integrate TMDC layers into heterostructures with different dielectric or
metallic substrates. This allows to tailor electronic and optical properties of
these materials, as Coulomb interaction inside atomically thin layers is very
susceptible to screening by the environment. Here we theoretically investigate
dynamical screening effects in TMDCs due to bulk substrates doped with carriers
over a large density range, thereby offering three-dimensional plasmons as
tunable degree of freedom. We report a wide compensation of renormalization
effects leading to a spectrally more stable exciton than predicted for static
substrate screening, even if plasmons and excitons are in resonance. We also
find a nontrivial dependence of the single-particle band gap on substrate
doping density due to dynamical screening. Our investigation provides
microscopic insight into the mechanisms that allow for manipulations of TMDC
excitons by means of arbitrary plasmonic environments on the nanoscale.
