  It is now well established that a high-frequency electromagnetic dressing
field within the off-resonance regime significantly modifies the electronic
transport and optical properties on Dirac materials. Here, using light with
circular polarization, we investigate its effect on the energy spectrum of
tilted monolayer 1T$^\prime$MoS$_2$ which acquires two energy gaps associated
with up- and down- pseudospin. We can adjust its electronic properties over a
wider range by varying these two band gaps in contrast with graphene. With the
use of the Lindhard approach for the frequency-dependent polarizability
propagator, we have developed a rigorous theoretical formalism for employing
the Floquet energy spectrum for investigating the many-body effects on the
plasmon excitations, their lifetimes due to Landau damping and the exchange
energy of tilted monolayer 1T$^\prime$MoS$_2$ under normal incidence of
electromagnetic radiation at arbitrary temperature. The dressed states at very
low temperature corresponding to circular polarization suppress the response of
the system to the external probe. This gives rise to the weak but long lived
plasmon excitations at small wavenumber $q$ when compared to the plasmon
spectrum in this regime in the absence of irradiation. However,
$\sqrt{qT}$-dependent plasmons are restored at high temperatures. Our
calculations have shown that the tilting, anisotropy, direct and indirect band
gaps lead to a reduced exchange energy, which has some potential applications
such as, tunability of exciton polariton and plasmon excitations.
