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Hyperbolic (or indefinite) materials have attracted significant attention dueto their unique capabilities for engineering electromagnetic space andcontrolling light propagation. A current challenge is to find a hyperbolicmaterial with wide working frequency window, low energy loss, and easycontrollability. Here, we propose that naturally existing electride materialscould serve as high-performance hyperbolic medium. Taking the electride Ca$_2$Nas a concrete example and using first-principles calculations, we show that thematerial is hyperbolic over a wide frequency window from short-wavelength tonear infrared. More importantly, it is almost lossless in the window. Weclarify the physical origin of these remarkable properties, and show itsall-angle negative refraction effect. Moreover, we find that the opticalproperties can be effectively tuned by strain. With moderate strain, thematerial can even be switched between elliptic and hyperbolic for a particularfrequency. Our result points out a new route toward high-performance naturalhyperbolic materials, and it offers realistic materials and novel methods toachieve controllable hyperbolic dispersion with great potential forapplications.

Tunable Hyperbolic Dispersion and Negative Refraction in Natural Electride Materials