Tunable in-plane bihyperbolicity in bismuth monolayer

The distinctive hyperbolic properties of natural two-dimensional (2D) materials have garnered considerable attention in recent years due to their potential to surpass the limitations of metahyperbolic surfaces. It is essential to control hyperbolic regions and the sign of optical conductivities. This study introduces the concept of ``bihyperbolicity'' and establishes a critical connection between the semiconducting characteristics of 2D materials and their hyperbolic attributes. Through first-principles calculations, we illustrate the applicability of this strategy to materials such as the recently synthesized bismuth monolayer. The computations revealed that altering the type ($n$ type or $p$ type) of semiconducting bismuth monolayers can lead to a reversal of conductivity signs along two orthogonal directions, consequently enabling the precise regulation of hyperbolicity. The intriguing interplay between hyperbolicity and semiconductivity lays the foundation for crafting in-plane hyperbolic heterostructures using well-established semiconductor technologies. These heterostructures unlock a plethora of exotic optical phenomena, including negative refraction and negative reflection, thereby opening new horizons in optical engineering and device design.