  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^{\num{-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.
