Non-Hermitian Linear Electrooptic Effect in 3D materials

Here, we present an in-depth theoretical analysis of the linear electrooptic effect in low-symmetry three-dimensional (3D) conductive materials with large Berry curvature dipoles. Our study identifies two distinct kinetic contributions to the linear electrooptic effect: a gyrotropic Hermitian (conservative) piece and a non-Hermitian term that can originate optical gain. We concentrate on the study of 3D materials belonging to the 32 ($D_3$) point group subject to a static electric bias along the trigonal axis. Our investigation shows that doped trigonal tellurium has promising properties, with its gyrotropic electrooptic response offering the potential for realizing electrically-biased electromagnetic isolators and inducing significant optical dichroism. Most notably, it is demonstrated that under sufficiently large static electric bias, tellurium's non-Hermitian electrooptic response may lead to optical gain. Using first-principles calculations, it is shown that n-doped tellurium is particularly promising, as it can host significantly larger Berry curvature dipoles than the more common p-doped tellurium.