  We present a thermal device based on the near-field interaction between two
substrates made of a polar and a metal-insulator-transition material. As a
result of the temperature dependence of the optical properties, this device
acts as a thermal rectifier, implying a strong asymmetry in the heat flux when
reversing the two temperatures. By covering both substrates with a graphene
sheet we show a significant enhancement of rectification coefficient. By
investigating the flux spectral properties along with its distance dependence,
we prove that this enhancement is associated to a change in the power-law
dependence of heat flux with respect to the separation distance in the
electrostatic regime due to the presence of graphene sheets. Our results
highlight the promising role of graphene-based hybrid structures in the domain
of nanoscale thermal management.
