  We study the radiative heat transfer between multilayer structures made by a
periodic repetition of a graphene sheet and a hexagonal boron nitride (hBN)
slab. Surface plasmons in a monolayer graphene can couple with a hyperbolic
phonon polaritons in a single hBN film to form hybrid polaritons that can
assist photon tunneling. For periodic multilayer graphene/hBN structures, the
stacked metallic/dielectric array can give rise to a further effective
hyperbolic behavior, in addition to the intrinsic natural hyperbolic behavior
of hBN. The effective hyperbolicity can enable more hyperbolic polaritons that
enhance the photon tunneling and hence the near-field heat transfer. However,
the hybrid polaritons on the surface, i.e. surface plasmon-phonon polaritons,
dominate the near-field heat transfer between multilayer structures when the
topmost layer is graphene. The effective hyperbolic regions can be well
predicted by the effective medium theory (EMT), thought EMT fails to capture
the hybrid surface polaritons and results in a heat transfer rate much lower
compared to the exact calculation. The chemical potential of the graphene
sheets can be tuned through electrical gating and results in an additional
modulation of the heat transfer. We found that the near-field heat transfer
between multilayer structure does not increase monotonously with the number of
layer in the stack, which provides a way to control the heat transfer rate by
the number of graphene layers in the multilayer structure. The results may
benefit the applications of near-field energy harvesting and radiative cooling
based on hybrid polaritons in two-dimensional materials.
