We demonstrate the existence and propagation of three hybrid modes of surface plasmon polaritons supported by two graphene monolayers coating a solid film. These modes propagate long distances with short wavelengths, which are suitable features to enhance the heat conduction along the film interfaces. For a 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 $\text{W}{\text{m}}^{-1}{\mathrm{K}}^{-1}$, which represents $67\%$ $(26\%)$ of its phonon Si $(\mathrm{Si}+\mathrm{graphene})$ counterpart. This thermal energy appears due to the coupling of plasmons propagating at speeds comparable to the speed of light in vacuum. The plasmonic heat conduction driven by two-dimensional materials thus appears as a major and unexpected mechanism for controlling temperature in solid-state systems at rates faster than the ones of phonons and electrons.

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• Surface plasmon polariton
• Thermal conductivity
• Graphene