r-BN: A fine hyperbolic dispersion modulator for bulk metamaterials consisting of heterostructured nanohybrids of h-BN and graphene

Hyperbolic metamaterials involving artificially crafted subwavelength structures uniquely interact with light to give extraordinary properties not found in nature. However, both predicting metamaterial candidates and realizing them are extremely challenging. Preparation processes typically require cutting-edge nanofabrication techniques and are frequently technically or intrinsically impossible. The reported hyperbolic metamaterial systems are merely two-dimensional or assembly of nanostructures. Herein, we report a facile design principle and exemplary fabrication for bulk metamaterials exhibiting tunable hyperbolic dispersions. They are uniquely formed by spontaneous self-assembly reaction between two surface-modified building blocks of few-layer-graphene (FLG) and exfoliated hexagonal boron nitride (h-BN) lamellae. Their mixing ratio, namely, the chemical composition of the bulk materials, is a delicate means of controlling hyperbolic responses. Remarkably, a small amount of rhombohedral BN (r-BN) further finely modulates both type-I and type-II hyperbolic dispersions both along in-plane and out-of-plane directions of the bulk materials. The permittivity of our bulk materials obtained by Kramer-Kronig relation exhibits their capability in negative refraction of incident light, and is delicately altered by the introduction of r-BN and the change in the composition of the FLG and h-BN building blocks both along in-plane and out-of-plane directions of the bulk materials. In other words, r-BN serves a role as a “dopant” in our h-BN/FLG metamaterials, significantly changing properties of bulk systems. Our achievement can be a new platform to readily design and synthesize bulk metamaterials without complicated preparation methods. It also presents that chemical compositions in our bulk metamaterial system are a facile and predictable means of controlling their properties, striking contrast to conventional metamaterials.