Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial

Abstract

Hexagonal boron nitride (h-BN) is a natural hyperbolic material¹, in which the dielectric constants are the same in the basal plane (ε^t ≡ ε^x = ε^y) but have opposite signs (ε^tε^z < 0) in the normal plane (ε^z)^1,2,3,4. Owing to this property, finite-thickness slabs of h-BN act as multimode waveguides for the propagation of hyperbolic phonon polaritons^1,2,5—collective modes that originate from the coupling between photons and electric dipoles⁶ 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^1,2,7. Here we show, by direct nano-infrared imaging, that these hyperbolic polaritons can be effectively modulated in a van der Waals heterostructure⁸ composed of monolayer graphene on h-BN. Tunability originates from the hybridization of surface plasmon polaritons in graphene^{9,10,11,12,13} with hyperbolic phonon polaritons in h-BN^1,2, so that the eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon–phonon polaritons. 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 can be classified as an electromagnetic metamaterial¹⁴ as the resulting properties of these devices are not present in its constituent elements alone.