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

Influence of Dynamical Floquet Spectrum on the Plasmon Excitations and Exchange Energy of tilted monolayer 1T$^\prime$MoS$_2$