$\mathrm{Mo}{\mathrm{Te}}_2$ as a natural hyperbolic material across the visible and the ultraviolet region

Hyperbolic materials are of particular interest for the next generation of photonic and optoelectronic devices. Since artificial metamaterials are intrinsically limited by the size of their nanostructured components, there has been a hunt for natural hyperbolic materials in the last few years. In a first-principles work based on density-functional theory and many-body perturbation theory, we investigate the fundamental dielectric response of $\mathrm{Mo}{\mathrm{Te}}_2$ in monolayer, bilayer, and bulk form and find that it is a natural type-II hyperbolic material with low losses between 3 and 6 eV. Going from the monolayer to the bulk, the energy window of hyperbolic dispersion is blueshifted by a few tenths of an eV. We show that excitonic effects and optical anisotropy play a major role in the hyperbolic behavior of $\mathrm{Mo}{\mathrm{Te}}_2$. Our results confirm the potential of layered materials as hyperbolic media for optoelectronics, photonics, and nanoimaging applications.

Figure 1

Side (left) and top (right) view of bulk $2\mathrm{H}-\mathrm{Mo}{\mathrm{Te}}_2$. Mo atoms are indicated in purple, Te atoms in gold. The unit cell is marked by dashed lines.

Figure 2

Quasiparticle band structures of ML (top), BL (middle), and bulk (bottom) $\mathrm{Mo}{\mathrm{Te}}_2$ including SOC. The highest occupied and lowest unoccupied bands are marked in green and red, respectively. The black arrows indicate the fundamental gap between the top of the valence band (set at zero energy) and the bottom of the conduction band.

Figure 3

Imaginary (top) and real (bottom) parts of the in-plane (left) and the out-of-plane components (right) of the imaginary (top) and real part (bottom) of the macroscopic dielectric function of ML, BL, and bulk $\mathrm{Mo}{\mathrm{Te}}_2$. The insets in the right panels magnify the regions where $\mathrm{Im}{\epsilon }_M$ in the ML and BL is significantly smaller compared to the bulk. The inset in the lower left panel highlights the region in which $\mathrm{Re}{\epsilon }_M$ changes sign. A Lorentzian broadening of 82 meV is applied to mimic excitation lifetimes.

Figure 4

(Left) Hyperbolic energy windows of $\mathrm{Mo}{\mathrm{Te}}_2$ in the bulk, BL, and ML form indicated by the horizontal bars. The background rainbow is indicative of the visible range. (Right) In-plane and out-of-plane component of the loss function for bulk $\mathrm{Mo}{\mathrm{Te}}_2$. A Lorentzian broadening of 82 meV accounts for excitation lifetimes.

Figure 5

Imaginary and real part of the macroscopic dielectric function of ML $\mathrm{Mo}{\mathrm{Te}}_2$ obtained including excitonic effects (BSE) and neglecting them (RPA). In the bottom panels, the shaded areas highlight the hyperbolic window. A Lorentzian broadening of 82 meV is applied to account for excitation lifetimes.