Broadband type-I hyperbolicity independent of carrier density in $\mathrm{RuOC}{l}_2$ crystals

The design and fabrication of hyperbolic metamaterials require precise control over the arrangement and dimensions of constituent components, such as nanosheets or nanowires, to achieve the desired hyperbolic dispersion. However, the ongoing challenge lies in further downsizing these components to broaden the hyperbolic regime and enhance the maximal wave vector. In this study, we propose a linear quasi-one-dimensional electron gas array model as a promising category of type-I natural hyperbolic materials (NHMs). The hyperbolic properties in these NHMs remain insensitive to the position of the Fermi level, owing to the linear dispersion relation near the Fermi level. Through first-principles calculations, we have identified a highly promising candidate material, the $\mathrm{RuOC}{l}_2$ crystal, for this model. Our research demonstrates that the $\mathrm{RuOC}{l}_2$ crystal exhibits a broad type-I hyperbolic region that spans from the infrared to the entire visible spectrum, and this property is nearly independent of the Fermi level's position, or equivalently, the carrier density. We also investigate the exceptional negative refraction effects and directional-propagating surface plasmon polaritons that arises from the hyperbolic equifrequency contour. These findings offer a universal approach to designing type-I NHMs, as well as a compelling foundation for development of cutting-edge optoelectronic devices.