Natural Hyperbolic Dispersion in Anisotropic Bulk and Nanoscaled Copper Chalcogenides.

Hyperbolic media support high-k electromagnetic modes, enabling subdiffractional confinement, anomalous refraction, and enhanced light-matter interactions. While most hyperbolic metamaterials rely on artificial structuring, natural hyperbolicity arises from crystal anisotropy and direction-dependent plasma frequencies. Here we provide direct experimental evidence for natural hyperbolicity in copper chalcogenides by spectroscopic ellipsometry in the visible-near-infrared range. We demonstrate hyperbolic dispersion in bulk covellite CuS by identifying a spectral window where the real parts of the in-plane and out-of-plane permittivity components have opposite signs. The study is then expanded to size-controlled CuS nanosheets as oriented films. Using the Bruggeman effective medium approximation to account for the nanostructure/void composite, we show that hyperbolicity persists upon nanoscaling and that the epsilon-near-zero condition and hyperbolic bandwidth shift with size. Finally, we demonstrate analogous behavior in klockmannite CuSe nanosheets, establishing copper chalcogenides as a tunable platform for natural hyperbolicity at the boundary of the NIR and visible ranges.