Transition metal dichalcogenide nanodisks as high-index dielectric Mie nanoresonators

Monolayer transition metal dichalcogenides (TMDCs) have recently been proposed as a unique excitonic platform for advanced optical and electronic functionalities. However, in spite of intense research efforts, it has been largely overlooked that, in addition to displaying rich exciton physics, TMDCs also possess a very high refractive index. This opens a possibility to utilize these materials for constructing resonant nanoantennas based on subwavelength geometrical modes. Here we show that nanodisks fabricated from exfoliated multilayer WS$_2$ support distinct Mie resonances and so-called anapole states that can be easily tuned in wavelength over the visible and near-infrared spectral range by varying the nanodisks' size and aspect ratio. We argue that the TMDC material anisotropy and the presence of excitons substantially enrich nanophotonics by complementing traditional approaches based on plasmonics and well-known high-index materials such as silicon. As a proof-of-concept, we demonstrate a novel regime of light-matter interaction, anapole-exciton polaritons, which we realize within a single WS$_2$ nanodisk. Our results thus suggest that nanopatterned TMDCs are promising materials for high-index nanophotonics applications with enriched functionalities and superior prospects.