  The material dependence of phonon-polariton based in-plane thermal
conductance is investigated by examining systems composed of air and several
wurtzite and zinc-blende crystals. Phonon-polariton based thermal conductance
varies by over an order of magnitude ($\sim 0.5-60$ nW/K), which is similar to
the variation observed in the materials corresponding bulk thermal
conductivity. Regardless of material, phonon-polaritons exhibit similar thermal
conductance to that of phonons when layers become ultrathin ($\sim 10$ nm)
suggesting the generality of the effect at these length-scales. A figure of
merit is proposed to explain the large variation of in-plane polariton thermal
conductance that is composed entirely of easily predicted and measured optical
phonon energies and lifetimes. Using this figure of merit, in-plane
phonon-polariton thermal conductance enlarges with increases in: (1) optical
phonon energies, (2) splitting between transverse and longitudinal mode pairs,
and (3) phonon lifetimes.

Materials Science