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Monolayer transition-metal dichalcogenides (ML-TMDs) offer excitingopportunities to test the manifestations of many-body interactions throughchanges in the charge density. Tuning the charge density by a gate voltageleads to profound changes in the optical spectra of excitons in ML-TMDs. Wereview the band-gap renormalization and dynamical screening as a function ofcharge density, and then incorporate these effects through variousapproximations that model long-wavelength charge excitations in theBethe-Salpeter Equation (BSE). We then show that coupling between excitons andshortwave charge excitations is essential to resolve several experimentalpuzzles.  Unlike ubiquitous and well-studied plasmons, driven by collectiveoscillations of the background charge density in the long-wavelength limit, wediscuss the emergence of shortwave plasmons that originate from the short-rangeCoulomb interaction through which electrons transition between the $\mathbf{K}$and $-\mathbf{K}$ valleys. We study the coupling between the shortwave plasmonsand the neutral exciton through the self-energy of the latter. We thenelucidate how this coupling as well as the spin ordering in the conduction bandgive rise to an experimentally observed optical sideband in electron-dopedW-based MLs, conspicuously absent in electron-doped Mo-based MLs or anyhole-doped ML-TMDs. While the focus of this review is on the opticalmanifestations of many-body effects in ML-TMDs, a systematic description of thedynamical screening and its various approximations allow one to revisit otherphenomena, such as nonequilibrium transport or superconducting pairing, wherethe use of the BSE or the emergence of shortwave plasmons can play an importantrole.

Dynamical screening in monolayer transition-metal dichalcogenides and its manifestations in the exciton spectrum