Polariton Heat Transport in Metals

This chapter is dedicated to the quantification and analysis of the thermal conductance and thermal conductivity of surface plasmon–polaritons propagating along a metallic nanofilm deposited on a substrate and a suspended nanofilm coated with graphene. This is done by deriving and analytically solving the plasmon dispersion relation for each structure. We show that the plasmon energy transport along the supported nanofilm is driven by two modes, while that along the graphene-coated nanofilm is guided by three modes. For a 1-cm-long gold nanofilm deposited on a silicon substrate, its two modes have comparable contributions and yield a maximum thermal conductivity of 15 Wm \({ }^{-1}\) K \({ }^{-1}\) , which is about 25 \(\%\) of its electron counterpart at 300 K, for a film thickness of 10 nm. On the other hand, for a graphene-coated Si film with a thickness of 15 nm and a length of 5 mm at 300 K, we find a plasmon thermal conductivity of 13.6 Wm \({ }^{-1}\) K \({ }^{-1}\) , which represents \(67\%\) ( \(26\%\) ) of its phonon Si (Si \(+\) graphene) counterpart. This thermal energy of both nanofilm configurations appears due to the coupling of plasmons propagating at speeds comparable to the speed of light in vacuum. The plasmonic heat conduction shows thus up as a major mechanism for controlling temperature in solid-state systems at rates faster than the ones of phonons and electrons.