Electronic and hyperbolic dielectric properties of ZrS2/HfS2 heterostructures

In this paper we investigate the electronic and optical dielectric properties of lateral and vertical heterostructures composed of two-dimensional (2D) $\mathrm{Zr}{\mathrm{S}}₂$ and $\mathrm{Hf}{\mathrm{S}}₂$ monolayers based on density-functional theory. First, we show that the bulk and monolayer $\mathrm{Zr}{\mathrm{S}}₂$ and $\mathrm{Hf}{\mathrm{S}}₂$ as well as the vertical ${(\mathrm{Zr}{\mathrm{S}}₂)}_m/{(\mathrm{Hf}{\mathrm{S}}₂)}_n$ heterostructures are indirect band-gap semiconductors, while the lateral heterostructures exhibit an indirect to direct band-gap transition. Then we demonstrate that the optical properties of the bulk and monolayer $\mathrm{Hf}{\mathrm{S}}₂$ and $\mathrm{Zr}{\mathrm{S}}₂$ are strongly anisotropic; for the bulk $\mathrm{Hf}{\mathrm{S}}₂$ and $\mathrm{Zr}{\mathrm{S}}₂$, the in-plane components of the dielectric function are negative in a certain frequency band, where they can work as naturally hyperbolic metamaterials. Interestingly, the vertical heterostructures also possess a hyperbolic region, whose position and width can be tunable with the thickness ratio of constituents. It is also found that the $(\mathrm{Zr}{\mathrm{S}}₂)/(\mathrm{Hf}{\mathrm{S}}₂)$ vertical heterostructures can enhance spontaneous emission and about 100-fold improvement of the Purcell factor is obtained. These results prove the feasibility of 2D material heterostructures to realize tunable hyperbolic metamaterials; the heterostructures present a promising opportunity for the practical applications in light-generation technologies.