Topological and hyperbolic dielectric materials from chirality-induced charge-parity symmetry

Parity-time $(\mathcal{PT})$ symmetry, originally conceived for non-Hermitian open quantum systems, has opened an exciting avenue towards coherent control of light for significant applications. Here we propose a paradigm towards non-Hermitian photonics based on the charge-parity $(\mathcal{CP})$ symmetry, in which the charge conjugation and parity symmetries are broken individually but preserved jointly. Such a symmetry-breaking scheme induces a transition from dielectric to hyperbolic dispersions in chiral dielectrics, leading to lossless all-dielectric hyperbolic metamaterials. More interestingly, the $\mathcal{CP}$-symmetry transition represents a non-Hermitian topological phase transition that occurs at infinite energy and requires no explicit band gap closing. We further showcase broad applications of $\mathcal{CP}$-symmetric photonics such as an all-angle polarization-dependent beam splitter and enhanced spontaneous emission. The $\mathcal{CP}$ symmetry opens an unexplored pathway for non-Hermitian topological photonics by bringing new physics into strong chiral metamaterials, therefore providing a powerful tool for engineering many promising applications in photonics and other related fields.