Efficient high-harmonic generation in van der Waals ferroelectric NbOI$_2$ crystals

Abstract

Layered NbOX$_2$ ($X=\mathrm{Cl,\,Br,\,I}$), a member of the van der Waals ferroelectric family, exhibits intrinsic ferroelectricity and pronounced nonlinear optical responses, making it a promising candidate for integrated nanophotonics applications. While previous studies have emphasized the material's strong second-order nonlinear responses, higher-order nonlinear responses are still mostly unexplored. This work systematically investigates NbOI$_2$ using high harmonic generation (HHG) spectroscopy. Driven by an intense mid-infrared laser field centered at $\sim4~μ\mathrm{m}$ wavelength, highly anisotropic odd- and even-order harmonics up to the 16th order are generated at a low peak intensity of $0.4~\mathrm{TW\,cm^{-2}}$, extending beyond the material's bandgap. Both bulk and flake forms of NbOI$_2$ display pronounced harmonic emission from the near-infrared to the deep-ultraviolet spectral region, with a notably high overall conversion efficiency compared to other known materials. Polarization-resolved measurements reveal that even-order harmonics remain aligned with the crystal polar axis regardless of the driving-field orientation, whereas odd-order harmonics are dynamically affected. First-principles calculations suggest that the flat valence band associated with Peierls dimerization enhances HHG efficiency through electron correlation. These findings provide fresh perspectives on HHG in van der Waals ferroelectric materials and facilitate the development of compact and tunable quantum light sources.

Figures (5)

• Figure 1: Schematic atomic structure of NbOI$_2$ and illustration of the experimental setup.a Front view of the crystal structure of NbOI$_2$ (space group, $C2$), Nb (blue), O (red), and I (pink) atoms form quasi-2D layers stacked along the a axis. b Top view of NbOI$_2$ along the $a$ axis. The crystal possesses in-plane intrinsic ferroelectricity, such that the $b$ and $c$ directions correspond to the polar and nonpolar directions, respectively. Nb-Nb atoms along the $c$ axis undergo Peierls dimerization, resulting in a $2 \times 1$ superstructure. The lattice geometry projected onto the bc plane reveals a network closely resembling a Lieb lattice. c Schematic illustration of mid-infrared transmission HHG spectroscopy in NbOI$_2$, with odd- and even-order harmonics generated and collected from the back surface of the crystal.
• Figure 2: Measured high-harmonic generation (HHG) spectra, intensity dependence of different harmonic orders from a bulk NbOI$_2$ crystal. a High-harmonic spectra from bulk NbOI$_2$ driven at a central wavelength of 4 $\mu$m. Blue/red curves correspond to the driving beam oriented along the polar/nonpolar axis, respectively. b,c Measured individual harmonic yield as a function of peak pump intensity $I$ (dots), with the driving laser oriented along the polar($b$) and nonpolar($c$) axes of the sample, respectively. Experimental data are fitted based on the power law $I^{p}$ (solid lines). The behavior strongly deviates from that expected for a perturbative nonlinear response with $p=q$ (dashed lines, scaled to the experimental data at the lowest intensity).
• Figure 3: Measured HHG spectra and related harmonic efficiency from three different thicknesses of NbOI$_2$. High-harmonic spectra obtained from NbOI$_2$ samples of varying thicknesses with the driving laser oriented along the a polar and b nonpolar axes of the sample, respectively. c--e Harmonic generation efficiency for each harmonic order from 4th to 16th for samples with different thicknesses.
• Figure 4: High-harmonics intensity from a NbOI$_2$ crystal as a function of the driving orientation and the generating harmonics orientation.a HHG spectra as a function of the orientation angle of the laser polarization relative to the polar optic axis in a 30 $\mu$m-thick NbOI$_2$ sample driven at 4 $\mu$m. The harmonics exhibit maxima (and minima) every 90$^\circ$ of rotation. Intensity is shown in false color on a logarithmic scale (arbitrary units). b Normalized harmonic intensities for the perpendicular configuration, obtained by integrating the corresponding spectral regions. c HHG polarization measurements as a function of the orientation angle of the laser polarization relative to the polar optic axis. Each spectrogram corresponds to a specific harmonic order, as labelled in the figure. Intensity is shown in false color on a logarithmic scale (arbitrary units). 0$^\circ$ corresponds to the polar axis of the sample.
• Figure 5: Calculated Band Structure and HHG Spectra of NbOI$_2$.a HSE-calculated band structure of monolayer NbOI$_2$ with orbital projection. A flat band predominantly derived from Nb bonding states near $E_f$ is separated by a gap from higher conduction bands. b The related density of states of NbOI$_2$, which reveals a pronounced peak from the Nb orbital near the $E_f$. c, d The numerically calculated HHG spectra along the polar/nonpolar directions, respectively. The HHG spectra were separated into interband and intraband contributions for driving orientation along polar direction in e and nonpolar direction in f, respectively.