Computational discovery of high-refractive-index van der Waals materials: The case of HfS$_2$

TL;DR

This work presents a pipeline combining high-throughput density functional theory screening with advanced many-body corrections to identify high-refractive-index van der Waals dielectrics suitable for visible photonics, validated by imaging ellipsometry and nanodisk Mie resonators. Hafnium disulfide (HfS$_2$) is highlighted as a standout, with an in-plane refractive index $n_\mathrm{in} > 3$ and strong anisotropy, while exhibiting low optical losses ($k$ small) in the visible; these predictions are corroborated experimentally and through finite-element simulations of nanodisks that reveal dipole and higher-order Mie resonances. The study also documents chemical instability of HfS$_2$ under ambient conditions, mitigated by storage in Argon or humidity-reduced environments, and demonstrates practical nanofabrication routes to harness its photonic properties. Overall, the paper validates a scalable computational-experimental framework for discovering high-index optical materials and positions HfS$_2$ as a promising platform for visible-range nanophotonics and metastructures.

Abstract

New high-refractive-index dielectric materials may enhance many optical technologies by enabling efficient manipulation of light in waveguides, metasurfaces, and nanoscale resonators. Van der Waals materials are particularly promising due to their excitonic response and strong in-plane polarizability. Here we combine ab initio calculations and experiments to discover new high-refractive-index materials. Our screening highlights both known and new promising optical materials, including hafnium disulfide (HfS$_2$), which shows an in-plane refractive index above 3 and large anisotropy in the visible range. We confirm these theoretical predictions through ellipsometry measurements and investigate the photonic potential of HfS$_2$ by fabricating nanodisk resonators, observing optical Mie resonances in the visible spectrum. Over the course of seven days, we observe a structural change in HfS$_2$, which we show can be mitigated by storage in either argon-rich or humidity-reduced environments. This work provides a comparative overview of high-index van der Waals materials and showcases the potential of HfS$_2$ for photonic applications in the visible spectrum.

Figures (5)

• Figure 1: vdW materials in optics. In-plane refractive index for the most commonly used vdW materials in optics along with the new TMDC HfS$_2$ discovered in this work. Refractive index data are obtained from Ref. Lee2019Munkhbat2022Vyshnevyy2023Zotev2023Polyanskiy2024 and plotted in the energy range where the imaginary part of the refractive index, i.e. the extinction coefficient, is below 0.1.
• Figure 2: Identification of high-refractive-index vdW materials. (a) Static in-plane refractive index as a function of direct band gap energy for 72 anisotropic semiconductor materials along with the Moss formula. Chemical formulas are provided for all of the super-Mossian materials. (b) Computed (dashed lines) and experimentally measured (solid lines) in-plane (red) and out-of-plane (blue) refractive indices. The in-plane and out-of-plane extinction coefficients are also plotted in green and grey, respectively.
• Figure 3: Mitigating the chemical instability of HfS$_2$. (a) Optical image of a HfS$_2$ flake right after exfoliation. (b) Optical image of the same HfS$_2$ flake after being exposed to ambient conditions for 29 days. Colour and structural (bubbles) changes are observed. (c) Height change (in nm) as a function of time (in hrs) for three different HfS$_2$ flakes. Their initial heights are 275.8, 63.1, and 188.6 nm respectively. (d) Growth (in %) as a function of time after exfoliation (in hrs). The growth is computed as increment of height over the current height. (e) Reflectance as a function of the wavelength and time after exfoliation for the flake with an initial height $H_0=188.6$ nm. (f) Comparative reflectance of a HfS$_2$ flake 5 hrs and 745 hrs after it was exfoliated. The flake is kept in a desiccator with a humidity reduced to 10%. The data is normalized with respect to the substrate.
• Figure 4: Fabrication of optical HfS$_2$ resonators. (a) The fabrication process consists of exfoliation, resist spin-coating, electron-beam lithography and argon etching. (b) Dark-field optical image at a 100x magnification of a series of HfS$_2$ nanoresonators with nominal diameters ranging from 260 to 350 nm in steps of 10 nm. A nanoresonator with a nominal diameter of 310 nm is encircled in red and imaged with scanning electron microscopy in (c). (d) Three-dimensional plot of a height measurement using an AFM. Both (c-d) reveal residual resist on top of the nanoresonator and redeposition of HfS$_2$ on the sidewalls. (e) AFM height measurement along a transverse line for the same resonator as (d), indicating the nominal diameter of 310 nm. The residual resist thickness and actual diameter are also indicated.
• Figure 5: Mie resonances in HfS$_2$ nanodisks. (a) Dark-field scattering measurements of the fabricated nanodisks (see inset). Each row of the plot corresponds to the spectral scattering measurement of a single resonator with a different nominal diameter. All of the scattering measurements are normalized by the same background signal. (b) Numerical scattering cross section calculated for a HfS$_2$ disk with a varying diameter. The disk is placed on a 90 nm thick layer of silica on semi-infinite silicon (see inset). The colored-stars refer to three specific diameters, whose electromagnetic fields are plotted in (d-f) for $\lambda=630$ nm. (c) Normalized dark-field scattering measurements for six nanodisks with varying diameters. The zero scattering line of each plot is moved up one unit. The solid lines are measured right after the resonators are etched, while the dashed lines are measurements after the sample has been in a glovebox for 168 hrs, with a total of six hour subjected to ambient condition. (d-f) Electromagnetic scattered field at a wavelength of $\lambda=630$ nm for diameters $d=210$ nm, $d=300$ nm, and $d=350$ nm, respectively. The boxes are color-coded to match the colored stars in (b). The real part of the electric field in the $\widehat{\mathbf{x}}$ polarization is plotted as a colour map, and the magnetic field is plotted as red arrows.