Microscopic theory for a minimal oscillator model of exciton-plasmon coupling in hybrids of 2d semiconductors and metal nanoparticles

The common model to describe exciton-plasmon interaction phenomenologically is the coupled oscillator model. Originally developed for atomic systems rather than solid-state matter, this model treats both excitons and plasmons as single harmonic oscillators coupled via a constant which can be fitted to experiments. In this work, we present a modified coupled oscillator model specifically designed for exciton-plasmon interactions in hybrids composed of two-dimensional excitons, such as in a transition metal dichalcogenide (TMDC) monolayers and metal nanoparticles while maintaining the simplicity of the commonly applied coupled oscillator models. Our approach is based on a microscopic perspective and Maxwell's equations, allowing to analytically derive an effective exciton-plasmon coupling constant. Our findings highlight the importance of the spatial dispersion, i.e., the delocalized nature of TMDC excitons, necessitating the distinction between bright and momentum-dark excitons. Both types of excitons occur at different resonance energies and exhibit a qualitatively different coupling with localized plasmons. We find a strong coupling between the plasmon and momentum-dark excitons, while a weakly coupled bright exciton manifests as an additional, third peak in the spectrum. Consequently, we propose a realistic modeling of the primary spectral features in experiments incorporating three harmonic oscillator equations instead of the conventional two. However, we also shed light on the limitations of the three coupled oscillator model in describing the line shape of extinction and scattering cross section spectra.