  We present a self-consistent Maxwell-Bloch theory to analytically study the
interaction between a nanostructure consisting of a metal nanoparticle and a
monolayer of transition metal dichalcogenide. For the combined system, we
identify an effective eigenvalue equation that governs the center-of-mass
motion of the dressed excitons in a plasmon-induced potential. Examination of
the dynamical equation of the exciton-plasmon hybrid reveals the existence of
bound states with negative eigenenergies, which we interpret as excitons
localized in the plasmon-induced potential. The appearance of these bound
states in the potential indicates strong coupling between excitons and
plasmons. We quantify this coupling regime by computing the scattered light in
the near-field explicitly and identify signatures of strong exciton-plasmon
coupling with an avoided crossing behavior and an effective Rabi splitting of
tens of meV.
