# Tunable Hyperbolic Dispersion and Negative Refraction in Natural Electride Materials

## TL;DR

This paper demonstrates that natural electride materials like Ca$_2$N exhibit tunable, low-loss hyperbolic dispersion and negative refraction over a broad frequency range, offering promising applications in photonics.

## Contribution

It reveals that electride Ca$_2$N naturally exhibits wide-band hyperbolic behavior with low energy loss and tunability via strain, providing a new class of high-performance natural hyperbolic materials.

## Key findings

- Ca$_2$N$ is hyperbolic from short-wavelength to near-infrared.
- The material exhibits almost lossless hyperbolic dispersion.
- Strain can switch the optical properties between elliptic and hyperbolic.

## Abstract

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.