Topological hyperbolic metamaterials.

Hyperbolic metamaterial (HMM) is a unique type of anisotropic material that can exhibit metal and dielectric properties at the same time. This unique characteristic results in it having unbounded isofrequency surface contours, leading to exotic phenomena such as spontaneous emission enhancement and applications such as super-resolution imaging. However, at optical frequencies, HMM must be artificially engineered and always requires a metal constituent, whose intrinsic loss significantly limits the experimentally accessible wave vector values, thus negatively impacting the performance of these applications. The need to reduce loss in HMM stimulated the development of the second-generation HMM, termed active HMM, where gain materials are utilized to compensate for metal's intrinsic loss. With the advent of topological photonics that allows robust light transportation immune to disorders and defects, research on HMM also entered the topological regime. Tremendous efforts have been dedicated to exploring the topological transition from elliptical to hyperbolic dispersion and topologically protected edge states in HMM, which also prompted the invention of lossless HMM formed by all-dielectric material. Furthermore, emerging twistronics can also provide a route to manipulate topological transitions in HMMs. In this review, we survey recent progress in topological effects in HMMs and provide prospects on possible future research directions.