Hybrid photonic-plasmonic cavities have emerged as a new platform to increase light-matter interaction capable to enhance the Purcell factor in a singular way not attainable with either photonic or plasmonic cavities separately. In the hybrid cavities proposed so far, mainly consisting of metallic bow-tie antennas, the plasmonic gap sizes defined by lithography in a repeatable way are limited to minimum values approx 10 nm. Nanoparticle-on-a-mirror (NPoM) cavities are far superior to achieve the smallest possible mode volumes, as gaps smaller than 1 nm can be created. Here, we design a hybrid cavity that combines a NPoM plasmonic cavity and a dielectric-nanobeam photonic crystal cavity operating at transverse-magnetic (TM) polarization. The metallic nanoparticle can be placed very close (< 1 nm) to the upper surface of the dielectric cavity, which acts as a low-reflectivity mirror. We demonstrate through numerical calculations that this kind of hybrid plasmonic-photonic cavity architecture exhibits quality factors, Q, above 10^{3} and normalized mode volumes, V , down to 10^{ um{-3}}, thus resulting in high Purcell factors (FP approx 10^5), whilst being experimentally feasible with current technology. Our results suggest that hybrid cavities with sub-nm gaps should open new avenues for boosting light-matter interaction in nanophotonic systems.
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