Dual Optical Hyperbolicity of PdCoO$_2$ and PdCrO$_2$ Delafossite Single Crystals

Hyperbolic materials exhibit a very peculiar optical anisotropy with simultaneously different signs of the dielectric tensor components. This anisotropy allows the propagation of exotic surface-wave excitations like hyperbolic phonons and plasmon polaritons. While hyperbolic materials hold promise for applications in subwavelength photonics and enhanced light-matter interactions, their natural occurrence is limited to few materials, often accompanied by significant dielectric losses and limited hyperbolic spectral bandwidth. Focusing on PdCoO$_2$ and PdCrO$_2$ delafossite transition-metal oxides, in this paper we demonstrate their unique dual hyperbolic regimes: one localized around a phonon absorption in the mid-infrared spectral region, and the other extending into the visible range. Both hyperbolic regimes show exceptional properties including low dissipation and high hyperbolic quality factors. These results pave the way for innovative applications of delafossite layered metals in subwavelength photonics, imaging, and sensing.