Tunable Hyperbolic Dispersion and Negative Refraction in Natural Electride Materials

Hyperbolic (or indefinite) materials have attracted significant attention due to their unique capabilities for engineering electromagnetic space and controlling light propagation. A current challenge is to find a hyperbolic material with wide working frequency window, low energy loss, and easy controllability. Here, we propose that naturally existing electride materials could serve as high-performance hyperbolic medium. Taking the electride Ca$_2$N as a concrete example and using first-principles calculations, we show that the material is hyperbolic over a wide frequency window from short-wavelength to near infrared. More importantly, it is almost lossless in the window. We clarify the physical origin of these remarkable properties, and show its all-angle negative refraction effect. Moreover, we find that the optical properties can be effectively tuned by strain. With moderate strain, the material can even be switched between elliptic and hyperbolic for a particular frequency. Our result points out a new route toward high-performance natural hyperbolic materials, and it offers realistic materials and novel methods to achieve controllable hyperbolic dispersion with great potential for applications.