  Hexagonal boron nitride (h-BN) is a natural hyperbolic material, for which
the dielectric constants are the same in the basal plane (epsilon^t = epsilon^x
= epsilon^y) but have opposite signs (epsilon^t*epsilon^z < 0) from that in the
normal plane (epsilon^z). Due to this property, finite-thickness slabs of h-BN
act as multimode waveguides for propagation of hyperbolic phonon polaritons -
collective modes that originate from the coupling between photons and electric
dipoles in phonons. However, control of these hyperbolic phonon polaritons
modes has remained challenging, mostly because their electrodynamic properties
are dictated by the crystal lattice of h-BN. Here we show by direct
nano-infrared imaging that these hyperbolic polaritons can be effectively
modulated in a van der Waals heterostructure composed of monolayer graphene on
h-BN. Tunability originates from the hybridization of surface plasmon
polaritons in graphene with hyperbolic phonon polaritons in h-BN, so that the
eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon-phonon
polaritons. Remarkably, the hyperbolic plasmon-phonon polaritons in
graphene/h-BN suffer little from ohmic losses, making their propagation length
1.5-2.0 times greater than that of hyperbolic phonon polaritons in h-BN. The
hyperbolic plasmon-phonon polaritons possess the combined virtues of surface
plasmon polaritons in graphene and hyperbolic phonon polaritons in h-BN.
Therefore, graphene/h-BN structures can be classified as electromagnetic
metamaterials since the resulting properties of these devices are not present
in its constituent elements alone.
