Plasmonic detection of Rashba spin-orbit coupling in monolayer transition metal dichalcogenides

Rashba spin-orbit coupling (RSOC) induces strong momentum-dependent spin splitting and plays a crucial role in fields such as spintronics and topological photonics. We here theoretically investigate the collective excitations in monolayer transition-metal dichalcogenides (ML-TMDs) hosting RSOC, and conceive an approach to precisely quantify the strength of RSOC using plasmons. We determine the electron energy loss function (EELF) and plasmon dispersions for $n$-type ML-TMDs from the dynamic dielectric function in the framework of the standard random phase approximation. In this system, both optical and acoustic plasmon modes are observed in the EELF and plasmon dispersions. Moreover, the plasmonic and spectral properties are tunable by electron density and dependent on RSOC. Crucially, we identify a minimum energy gap between the two plasmon modes to serve as a direct spectral signature of the RSOC strength. These results establish plasmons as a noninvasive, precise, and broadly tunable technique for determining RSOC in TMD van der Waals heterostructures and devices.