Natural hyperbolicity in layered hexagonal crystal structures

Discovering the physical requirements for meeting indefinite permittivity in natural material as well proposing a new hyperbolic media offer possible route to significantly improve our knowledge and ability confine controlling light optoelectronic devices. We demonstrate hyperbolicity class of materials with hexagonal P6/mmm P6$_{3}$/mmc layered crystal structures its origin is thoroughly investigated. By utilizing density functional theory solving Bethe-Salpeter equation (BSE), we find that structure symmetry imposed constraints Li$_{3}$N gives rise an exceedingly strong anisotropy optical responses along in- out-of-plane directions crystals making it broad spectral range from visible spectrum ultraviolet. More excitingly, relation anisotropic interband absorption addition impressive dependency conduction band lattice constant direction provide tunability these under strain, doping, alloying. Our findings not only suggest large family real compounds unique realization highly tunable but also offers approach search