Hyperbolic localized plasmons and twist-induced chirality in an anisotropic 2D material

Domain: neuroscience
Published: 2026-02-13
Editorial outcome: minor_revision

Abstract
Two-dimensional (2D) van der Waals materials with strong in-plane anisotropy are emerging as fertile platforms for nanophotonics beyond conventional isotropic noble metals and dielectrics. Here, we demonstrate hyperbolic localized plasmon resonances (H-LPRs) in MoOCl2, a representative anisotropic 2D crystal. Unlike conventional plasmons, H-LPRs arise directly from the crystal anisotropy and show unprecedented properties: (i) one-dimensional resonances in circularly symmetric nanodisks, (ii) Z-gap independence in metal–insulator–metal heterostructures, and (iii) twist-induced chirality with circular dichroism values exceeding 0.65. The H-LPRs are characterized by both far-field spectra and near-field imaging. By stacking twisted MoOCl2 flakes, we bridge H-LPRs with concepts of moiré photonics and twistronics, introducing a new degree of freedom in plasmonic design. These findings establish H-LPRs in anisotropic 2D materials as a generalizable and versatile platform for polarization engineering, ultrasensitive chiral sensing, and integration into compact on-chip and quantum nanophotonic devices.

Introduction
Chirality and plasmonics underpin a wide range of technologies, from enantioselective sensing1 and drug development2 to photonic information processing3. However, existing plasmonic systems, which are largely based on isotropic noble metals4,5, lack the anisotropy that is required for robust chiral control and tunable light confinement. Light–matter interactions at the nanoscale are often engineered with plasmons in noble metals, which support surface plasmon polaritons6 and localized surface plasmon resonances (LSPRs)7,8. These modes enable field confinement and applications in sensing9, photocatalysis10,11, and information processing12,13. However, conventional LSPRs are limited by their isotropic permittivity and geometry-dependent resonance tuning.

The rise of layered van der Waals (vdW) materials with novel optical properties has provided new opportunities for nanophotonics14, such as materials with significant anisotropy15, strong nonlinearity16, as well as magnetically-dressed excitons17 and phonon polaritons18–22. Among them, natural hyperbolic materials—van der Waals crystals with anisotropic permittivity components of opposite signs—support hyperbolic polaritons, which are known for sub-wavelength confinement and directional propagation18–30. Hyperbolic polaritons have been widely investigated in phonon materials in the mid-infrared, such as hBN and α-MoO3. Recently, this research has been expanded to plasmon materials in the near-infrared and visible light31–36. However, how hyperbolic dispersion manifests in localized plasmon modes and their distinct properties has remained unexplored.

Here, we experimentally introduce hyperbolic localized plasmon resonances (H-LPRs) using layered MoOCl231–36. H-LPRs exhibit distinct properties: (i) one-dimensional resonances in symmetric disk metasurfaces, (ii) Z-gap independence in MoOCl2–insulator–metal stacks, and (iii) twist-induced chirality without breaking geometric symmetry. These unique features enable robust and broadband responses across the visible to near-infrared spectrum. By bridging hyperbolic polaritons and localized plasmons, H-LPRs provide a new nanophotonic toolkit for 2D vdW anisotropic plasmonics and twistronics, with implications for light-field control, polarization engineering, and practical chiral devices.

Results
Hyperbolic localized plasmon resonances
MoOCl2 is a layered van der Waals crystal with a monoclinic structure (space group C2/m)31,32 that exhibits pronounced in-plane anisotropy. The structure is strongly coupled along the Mo–O chains, while the inter-chain coupling in the orthogonal direction is significantly weaker. Along the Mo–O chain axis, the material is metallic (εx < 0), whereas the orthogonal directions remain dielectric (εy, εz > 0) across the visible to near-infrared spectrum (Fig. 1a, b)31,34,35,37. This unique permittivity landscape fundamentally distinguishes MoOCl2 from the isotropic noble metals that are typically used in plasmonics. A planar flake with a thickness of tens of nanometers supports hyperbolic plasmon polaritons, whose iso-frequency contours (IFCs) are hyperbolic in the in-plane direction (Fig. 1b), which is expressed as follows:

kx^2/εy + ky^2/εx = ω^2/c^2 (1)

When a MoOCl2 flake is patterned into an anodisk metasurface, a localized resonance mode emerges. The structural parameters, namely, the disk radius (R), thickness (H), and squared period (P), are defined in Fig. 1c. A representative transmission spectrum for R=80nm, H=60nm, and P=500nm under x-polarization shows a distinct resonance peak (Fig. 1d). The corresponding three-dimensional mode distribution (Fig. 1e, f) reveals strong electric fields that are localized at disk edges and surfaces, together with ray-like volumetric profiles inside the structure. Ray-like lines appear because most wavevectors are oriented along the asymptotes of the hyperbola, and their directions are determined by the open angle of the hyperbola. These volumetric ray-like features are hallmarks of hyperbolic dispersion35,38,39 and sharply contrast with the purely surface-confined fields of LSPRs in Au. It should be noted that the full 3D IFCs can be found in the literature33, showing an open-angle 3D hyperboloid. In addition, the ghost mode may have a weak contribution to the in-plane mode distribution33,38,40. More discussions on hyperbolic modes are provided in Supplementary Note 1.

The results of finite-difference time-domain (FDTD) simulations confirm that the mode volume of MoOCl2-based resonances is intrinsically larger than that of Au LSPRs of equivalent geometry. For instance, with the parameters of Fig. 1d, the calculated mode volume is V = ∫ E^2 dV / max(E^2) (2)

using the time-averaged electric field distributions obtained from FDTD calculations. The integration volume covers the entire meta-atom and its near-field region. Here, the ε is omitted due to its anisotropy. The obtained V ≈ 3.5 × 10^-4 λ^3, confirming the strong field confinement of the H-LPR. However, this value is approximately an order of magnitude greater than that of Au LSPRs, which originates from a volumetric hyperbolic distribution rather than surface confinement. Taken together, these results justify the definition of a new class of states, hyperbolic localized plasmon resonances (H-LPRs), which bridge the physics of delocalized hyperbolic polaritons and conventional localized plasmons.

To experimentally validate H-LPRs, we fabricated high-quality MoOCl2 nanodisk metasurfaces using electron-beam lithography and reactive ion etching, following iterative optimization. A representative scanning electron microscopy (SEM) image reveals homogeneous morphology across large areas (R=87nm, H=50nm, and P=500nm) (Fig. 2b). Optical images under reflective microscopy further highlight the anisotropy: under x-polarization, the disks exhibit a metallic golden luster, whereas under y-polarization they appear as dielectric films (Fig. 2c). Each metasurface array spans 50 μm × 50 μm with a designed disk radius. Unless otherwise specified, the x-polarization is aligned with the metallic chain axis.

The transmission spectra reveal clear resonances under x-polarization that redshift systematically with increasing disk radius (Fig. 2d). In sharp contrast, no resonance peaks are observed under y-polarization, where high transmittance persists across all disk sizes (Fig. 2e). To more precisely probe the polarization dependence, we measured the spectra as the polarizer was rotated from –90° to +90° (Fig. 2f). The corresponding differential spectra |T – T90°| highlight the resonance evolution, and the peak intensity variation follows Malus’s law (I = I0 cos^2 θ) (Fig. 2g, h). This angular dependence provides direct experimental evidence for the one-dimensional characteristic of the H-LPR mode, and the extinction ratio between x- and y-polarized excitations at 840 nm is approximately 11.5, confirming that the resonance is purely one-dimensional along the anisotropic axis.

FDTD simulations reproduce all of the observed spectral features, and further experiments on samples with various thicknesses and fabrication conditions confirm the reproducibility and robustness of the results (Supplementary Figs. 4–7). Importantly, this intrinsic one-dimensionality arises despite the highly circularly symmetric disk geometry and originates solely from the in-plane anisotropic permittivity of MoOCl2. Such 1D resonances in symmetric geometries open new opportunities for light-field control and polarization-sensitive detection and may be further engineered for mode coupling and modulation, as demonstrated in metallic LSPRs13,41,42 and dielectric metasurfaces43.

To further investigate the resonance properties of H-LPRs, we performed near-field characterizations using photoemission electron microscopy (PEEM) integrated with a tunable femtosecond laser beamline. This method has previously been used in the study of various near-field modes supported by metals and dielectrics8,41,44–48. The laser beam was incident at the normal angle, with the polarization controlled by a λ/2 waveplate. Near-field imaging in the near-infrared using PEEM relies on a multi-photon photoemission process to overcome the material’s work function. The nonlinear photoemission yield follows PE ∝ IN, where PE is the photoemission intensity, I is the local light intensity, and N is the nonlinear order (here, N = 4, as measured).

As shown in Fig. 3a, under x-polarization, the PEEM images exhibit strong photoemission signals, indicating the strong near-field enhancement of the localized modes (see enlarged PEEM images in Supplementary Fig. 8). In contrast, almost no signals can be observed under y-polarization. Sweeping the excitation wavelengths under constant laser power enables the photoemission yield spectra (near-field enhancement spectra) to be obtained. As illustrated in Fig. 3b, the near-field spectra are consistent with the far-field transmission spectra for both x- and y-polarizations, providing robust evidence for the 1D localized resonance characteristic of MoOCl2 disks.

Z-gap independence in metal–insulator–metal structures
To probe the out-of-plane response of H-LPRs, we fabricated MoOCl2/Al2O3/Au metal–insulator–metal (MIM) structures with controlled Al2O3 spacer thicknesses from 2.5 to 20 nm via atomic layer deposition (Fig. 4a–c). In conventional Au-based MIM systems, the resonance frequency strongly depends on the gap thickness because of the formation of highly confined gap modes. In contrast, the resonance wavelengths of the MoOCl2 MIMs remain nearly constant across this entire range of spacer thicknesses. The evolution of the peak wavelengths of the reflection spectra with increasing Al2O3 gap size (Fig. 4d) clearly demonstrates this invariance, thus establishing Z-gap independence as an intrinsic property of MoOCl2 H-LPRs.

Quantitatively, the resonance shift versus spacer thickness yields |dλ/dG| < 1.5 nm from 2.5 to 20 nm for MoOCl2 H-LPRs, whereas it reaches 101–102 nm for Au MIMs, clearly demonstrating the pronounced Z-gap independence. The results of numerical simulations corroborate the experimental data and clarify the physical mechanism (Fig. 4e). Along the z-axis, MoOCl2 has a positive permittivity (εz > 0)31 that closely matches that of Al2O3 (Fig. 4f), thereby suppressing the high-k gap modes that are responsible for the strong thickness dependence of noble-metal MIMs (Fig. 4g) (More discussion on gap mode versus z-axis permittivity are shown in Supplementary Note 6). In Au MIMs, the abrupt permittivity discontinuity across the spacer leads to strongly localized, thickness-sensitive resonances (Fig. 4g)49. The absence of such discontinuity in MoOCl2 explains the observed robustness. Importantly, compared with MoOCl2 disks directly on glass substrates, MIM structures exhibit resonance redshifts to longer wavelengths (e.g., an ~100 nm redshift for R=60 nm), which expands the spectral tunability of H-LPRs.

This Z-gap independence is technologically significant. It removes sensitivity to nanometer-scale fabrication tolerances, which is a common bottleneck for reproducible nanophotonic devices. Moreover, it enables scalable stacking of metasurfaces and heterostructures without precise spacer control, thereby facilitating the integration of H-LPRs into complex photonic architectures. Further comparisons of the spectral line shapes that confirm the invariance are provided in Supplementary Fig. 9.

Twist chirality in symmetric geometries
Chirality can be achieved by breaking the mirror symmetry of a structure. Various strategies, such as the assembly of unit structures by in-plane rotation5, the introduction of vertical tilt50,51 and structural twisting52–54, have been employed to construct chiral responses. Having established the 1D anisotropy and Z-gap independence, we sought to realize optical chirality by twisting the in-plane anisotropic permittivity axes of stacked MoOCl2 disks while maintaining circular symmetry (as illustrated in Fig. 5a). SEM and optical microscopy confirm high-quality fabrication with uniform alignment and negligible defects (Fig. 5b, c). Under left- and right-circularly polarized (LCP and RCP) excitation, the transmission spectra reveal resonance peak shifts that exceed 100 nm (Fig. 5d), and the corresponding circular dichroism (CD) values are >0.2, where CD is defined as CD = (TLCP − TRCP) / (TLCP + TRCP)51. These values are remarkable considering the fully symmetric disk geometry and rival or surpass those of engineered chiral metasurfaces that rely on explicit geometric asymmetry.

Simulations reproduce the experimental chirality and reveal its robustness against variations in the twist angle, thickness mismatch, and disk radius (Fig. 5e and Supplementary Note 7). For example, even when the upper and lower disk thicknesses deviate by tens of nanometers, the chiral response remains substantial (Supplementary Fig. 14). This robustness is consistent with an effective thickness model, in which LCP and RCP waves accumulate different optical path lengths because of opposite polarization rotations (Supplementary Note 7). The model predicts that the total effective thickness governs the degree of chirality, which explains why deviations in individual disk dimensions do not strongly reduce the effect. As shown in Fig. 5f, the different rotations of near-field modes when passing through the twist disks can be observed, for LCP and RCP light.

Beyond its robustness, twist-induced chirality is broadband and persists across visible to near-infrared wavelengths. Moreover, the metasurfaces support tunable polarization responses across the full Poincaré sphere by adjusting the twist parameters, thereby enabling complete polarization engineering (Fig. 5f). This functionality establishes H-LPR-based twist metasurfaces as promising platforms for ultrasensitive chiral sensing, broadband polarization control, and spin–photon interfaces. Detailed simulation studies of the twist angle dependence and experimental spectra from multiple samples with various thicknesses and radii are presented in (Supplementary Notes 7 and 8), which support the robustness of the chiral response, and the reproducibility was confirmed over five independent samples fabricated on separate substrates.

It should be noted that the present study does not intend to achieve the optimal chiral response. By designing the metasurface period, the in-plane geometric shape and the vertical multilayer stacking, it is possible to further engineer the chiral response. For example, the circular dichroism can be improved by reducing the metasurface period, as shown in Supplementary Fig. 21. The maximum circular dichroism exceeds 0.65 in simulations and 0.54 in experiments (P=350 nm). The CD enhancement arises from the increased density and stronger near-field coupling between adjacent disks as the period decreases, which effectively amplifies the asymmetric local field for LCP and RCP excitation. In addition, the comparisons of twisted MoOCl2 metasurfaces with twisted noble metal metasurfaces and twisted unpatterned MoOCl2 films are discussed in Supplementary Note 8.

Methods
Sample fabrication and characterizations
The MoOCl2 flakes were mechanically exfoliated on polydimethylsiloxane (PDMS) sheets from bulk crystals (Nanjing MKNANO Tech. Co., Ltd. (www.mukenano.com)), and the thicknesses of the MoOCl2 flakes were estimated by the reflected color under optical microscopy before transfer. The selected MoOCl2 flakes were transferred onto a substrate using the all-dry transfer method under optical microscopy. For single–disk and twist metasurfaces, soda-lime glass substrates with a ~10 nm ITO layer were used. For MIM metasurfaces, silica substrates were used. Each substrate was pre-marked with gold markers for positioning.

For single–disk metasurfaces, the usual process flow mainly includes electron-beam lithography (EBL) and reactive ion etching (RIE), with EB resist as a mask. Before EBL, an EB resist (ZEP520A:ZEP-A=1:1, Zeon Chemicals) was spin-coated onto the substrate with MoOCl2 flakes at 300 rpm for 3 s and 3000 rpm for 60 s. Next, the substrate was pre-baked at 180 °C for 2 min. The EBL system (ELS-F130HM, Elionix) operated at 130 kV with an electron current of 100 pA. After EBL, the sample was developed with ZED-N50 for 60 s and ZED-B for 10 s. Then, RIE (RIE-101iPH, Samco Inc.) was used to etch the MoOCl2 with SF6 gas. After RIE, the EB resist was cleanly removed using the lift-off (DMAC) process at 70°C for 20–30 min, without ultrasonication. Finally, the sample was cleaned with acetone and methanol. We also fabricated some samples with a hard mask of several-nm Ti. For those samples, a helicon sputtering (MPS-4000C1/HC1, ULVAC) and an ultrasonic lift-off process were used before the RIE process.

For twist metasurfaces, MoOCl2 flakes with similar thickness were pre-selected, and the twist angle was pre-defined during the transfer process. The surface of the lower MoOCl2 was cleaned to remove residue PDMS. After transfer, the sample was annealed under vacuum at 100–130°C for 20 min. These steps were intended to reduce interlayer bubbles. The subsequent steps are the same as those for single–disk metasurfaces with EB resist as a mask.

For MoOCl2 MIM metasurfaces, silica substrates with gold markers were used to sputter 100 nm Au, with 2 nm Ti as the adhesion layer. Then, Al2O3 layers were grown on the substrates using atomic layer deposition (ALD) at a rate of 1 nm/10 cycles (R-200 advanced, Picosun). Then, MoOCl2 flakes were transferred onto these Al2O3/Au/SiO2 substrates. The subsequent steps are the same as those for single–disk metasurfaces with EB resist as a mask.

After sample preparations, the samples were characterized using optical microscopy, scanning electron microscopy (SEM) (SU8230, Hitachi High-Technologies), and a thickness measuring instrument (ET200, Kosaka Laboratory, Ltd.).

Spectral measurements
The resonance modes of MoOCl2 metasurfaces were characterized using transmission or reflection spectra, with a home-built optical microscopy system equipped with a photonic multichannel analyzer (PMAC7473, Hamamatsu Photonics). A linear polarizer and a 1/4 λ waveplate were used to control the polarization states. For the reflection spectra, a silver mirror was used as the reference, and calibration was performed using the reflectance of silicon to obtain the actual spectra.

PEEM measurements
The PEEM measurements were performed on a high-resolution low-energy electron microscopy (LEEM)/PEEM system (ACSPELEEM III, Elmitec GmbH). A commercial Ti:sapphire femtosecond laser (MaiTai HP, Spectra-Physics, pulse duration: 80−100 fs) operated at 690−1040 nm (2.9 W @ 820 nm) with a repetition rate of 80 MHz was used to provide a tunable laser for PEEM measurements. The pulses were focused on the sample surface at normal incidence with a spot diameter of approximately 100 μm. The polarization of the laser was controlled by a λ/2 waveplate.

Simulations
The resonance modes of MoOCl2 metasurfaces were simulated using the finite-difference time-domain method (FDTD, Ansys Lumerical), using the measured permittivity (εx, εy) and theoretical permittivity (εz). The optical properties of Au were obtained from Johnson and Christy and the refractive index of the glass substrate was set to 1.5. For twist metasurfaces, the refractive index axes were rotated using the “permittivity rotation attribute” component. The excitation light was set to normal incidence with the required polarization states. The FDTD simulations well reproduced the experimental results.

Data availability
The data supporting the findings are displayed in the main text and the supplementary information. All raw data are available from the corresponding authors upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Li et al. describes the nanofabrication and investigation of arrays of nanostructured MoOCl2 realizing both hyperbolic localized plasmon resonances as well as chiral optical responses. Hyperbolic localized plasmon resonances have never been reported prior to this work and suggest a new opportunity for controlling and modifying MoOCl2 for nanophotonic applications. They authors also demonstrate that by creating at twisted MoOCl2 sample prior to nanofabrication they can achieve extremely strong circular dichroism even in a material that is otherwise isotropic in plane. Such research into anisotropic and hyperbolic materials, such as MoOCl2, is extremely important in the nanophotonics field as efforts have turned to using natural material anisotropy in order to control material properties.\nOverall the manuscript was well written, the analysis, interpretation and conclusions were largely sound. However, there are several additional major and minor points that should be addressed in revisions.\nMajor Points:\n1. The authors should address what benefits the twisted MoOCl2 provides over chiral noble metal nanostructures.\n2. The authors should be careful to note that in a biaxial medium there are always two propagating wave solutions (both extraordinary). The hyperbolic modes occur for only one root of the quartic wave equation. Do both roots play a role in the observed modes in the H-LPRs? (see Narimanov, E. E. Phys. Rev. A 98, 013818 (2018))\n3. In the text the manuscript states: \"Ray-like lines appear because most wavevectors are oriented along the asymptotes of the hyperbola, and their directions are determined by the open angle of the hyperbola.”\nThese ray-like modes seem to be attributed to “ghost modes” else where. See Narimanov, E. E. Phys. Rev. A 98, 013818 (2018) and Venturi et al. Such directional ghost modes show the unique character of having both propagating and evanescent character even without intrinsic material losses. Are the rays observed here due to the hyperbolic modes (defined by the hyperbolic isofrequency surface) or the ghost modes? I don't disagree that that these appear to be localized plasmon resonances in a hyperbolic material, the question becomes do they have truly hyperbolic dispersion or not.\n4. As discussed in the supplementary information increasing R redshifts the spectra while increasing H blueshifts the spectra. Could the authors explain why increasing H would increase the energy of the hyperbolic mode? It seems that thin film models of surface plasmonic behavior could explain this in a quite straightforward fashion without needing to invoke a hyperbolic mode.\nMinor Points:\n1. Figures 2d and e, please clarify more in the figure itself that the spectra are being plotted versus disk radius.\n2. Figure 3 is confusing. It was hard to tell which of the subpanels were which polarizations and smaller FOVs at first glance. I would recommend modifying the arrangement of the panels and perhaps being more selective on which panels are displayed in the main text.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "Comments about NCOMMS-25-92838-T\nIn this work, the authors report hyperbolic localized plasmon resonances in the two-dimensional material MoOCl2, which exhibits strong in-plane anisotropy, and introduce twist-induced chirality in geometrically symmetric metasurfaces. The observed plasmon resonances feature one-dimensional confinement, z-gap independence, and pronounced circular dichroism arising from twist-induced chirality. However, promising hyperbolic media are expected to exhibit high electromagnetic confinement, low energy loss, and flexible tunability under external fields. The hyperbolic MoOCl2 system does not offer any fundamentally new advantages in electromagnetic confinement, energy loss and tunability, compared with previously reported materials such as MoO3, h-BN, WTe2, Ga2O3 and black phosphorus, all of which have already been extensively studied for supporting hyperbolic polaritons. In addition, the current experimental data set is incomplete and insufficient to support the major claims making it difficult to evaluate the robustness of the conclusions. As a result, the novelty of this work appears limited for publication in Nature Communications and would be more suitable for a specialized journal.\nComments:\n1. The authors claim that MoOCl₂ exhibits one-dimensional characteristics in its hyperbolic localized plasmon resonances. However, one-dimensional materials are generally composed of 1D structural units connected by weak van der Waals interactions, which is not clearly illustrated or discussed in Fig. 1a. Clarification on the structural origin of this claimed one-dimensionality is necessary.\n2. In Fig. 1b, the real part of the permittivity appears to vary almost linearly with wavelength, which seems unusual for 2D materials. It would be necessary to also provide the imaginary part of the optical dielectric function, as the real and imaginary components should satisfy the Kramers–Kronig relation. Including this information would help verify the physical consistency of the presented optical data. If experimental measurements are challenging, first-principles calculations could also be provided to support and better interpret the observed results.\n3. The physical origin of the observed hyperbolicity should be clarified. In particular, the respective roles of interband and intraband transitions, which are crucial for producing strong optical anisotropy and hyperbolic dispersion, need to be discussed in greater detail. Providing this analysis would help elucidate the microscopic mechanism underlying the reported hyperbolic behavior. Similar discussions has been reported in Nat Commun 11, 1158 (2020).\n4. The presented hyperbolic isofrequency contours appear incomplete. Additional data points at a wider range of frequencies should be included to clearly illustrate the frequency range over which hyperbolicity occurs, as well as the transition from elliptic to hyperbolic dispersion. This would provide a more comprehensive understanding of the material's optical anisotropy and dispersion characteristics.\n5. The wavelength ratio of the hyperbolic in-plane dispersion to the corresponding free-space photon wavelength (i.e., electromagnetic confinement) should be provided, along with the propagation length and lifetime of the hyperbolic polaritons. These parameters are essential for quantitatively evaluating the performance and quality of hyperbolic materials.\n6. Plasmon hyperbolic materials often exhibit higher losses, a short discussion on loss mechanisms in MoOCl2, including thickness dependence and Q-factor of H-LPRs would help readers assess performance limits and potential device implications.\n7. The manuscript states that chirality is robust to thickness mismatch and fabrication variations, but it would help to quantify the tolerance (percent-level deviations in thickness or twist angle).\n8. Can the authors elaborate on the microscopic origin of the twist-induced chirality, possibly through a brief tensor-transformation argument for the rotated permittivity?\n9. Would chirality persist in multilayer twist stacks (beyond bilayers), and if so, does the effective thickness model remain applicable?", "reviewer_4": "This manuscript reports the discovery and experimental demonstration of the hyperbolic localized plasmon resonances (H-LPRs) in the anisotropic two-dimensional van der Waals material MoOCl₂. H-LPRs originate from the intrinsic in-plane anisotropic permittivity (metallic along the Mo-O chain axis, dielectric in orthogonal directions), leading to hyperbolic iso-frequency contours. H-LPRs exhibit three important properties: one-dimensional resonance, Z-gap independence and twist-induced chirality. These properties are validated through far-field spectroscopy, near-field photoemission electron microscopy imaging, and comprehensive simulations. Overall, the manuscript is clearly written and the topic is of interest. However, prior to publication, several issues should be addressed:\n1.The authors attribute Z-gap independence to the matching permittivity between MoOCl₂ and Al₂O₃. Could a more quantitative analysis be provided to explain why the high-k gap modes is strongly suppressed, leading to insensitivity to gap thickness?\n2.For anisotropic 2D materials (e.g., α-MoO₃), studies have shown that significant circular dichroism can be achieved by directly stacking two flakes with a twist angle. If two pristine, unpatterned MoOCl₂ flakes are stacked with a twist, what would be the expected CD value of such a system? Is fabricating a metasurface to obtain H-LPRs a necessary condition for achieving the strong chirality?\n3.To demonstrate hyperbolic properties, the inset in Fig. 1b only emphasizes the hyperbolic in-plane isofrequency contours (xy-plane). However, in Fig. 1f, the ray-like electric field distribution, which is a hallmark of hyperbolicity, appears to be stronger out-of-plane (xz-plane). Does this suggest that the one-dimensional resonance characteristic stems from both in-plane and out-of-plane hyperbolic properties?\n4.Lines 78-80 of the manuscript state: \"These volumetric ray-like features are...sharply contrast with the purely surface-confined fields of LSPRs in Au.\" For a more intuitive and direct comparison, it would be helpful to provide simulated electric field distributions for Au LSPRs.\n5.In the introduction, when discussing hyperbolic polaritons, the reviewer recommends citing Nature Communications 11, 1158 (2020), which reports WTe₂ as another hyperbolic material and is relevant to the context."}, "author_response": "Point-by-point reply to the reviewers' comments.\nWe thank the reviewers for their careful reviewing of our manuscript and for their\ndetailed and constructive reports. During the revision, we have taken all the comments\nfrom the reviewers into consideration. Our responses to each of the reviewers’\ncomments are as follows and highlighted in blue, and the revisions in the new\nmanuscript are highlighted in red.\nReviewer #1 (Remarks to the Author):\nThe manuscript by Li et al. describes the nanofabrication and investigation of arrays of\nnanostructured MoOCl2 realizing both hyperbolic localized plasmon resonances as\nwell as chiral optical responses. Hyperbolic localized plasmon resonances have never\nbeen reported prior to this work and suggest a new opportunity for controlling and\nmodifying MoOCl2 for nanophotonic applications. They authors also demonstrate that\nby creating at twisted MoOCl2 sample prior to nanofabrication they can achieve\nextremely strong circular dichroism even in a material that is otherwise isotropic in\nplane. Such research into anisotropic and hyperbolic materials, such as MoOCl2, is\nextremely important in the nanophotonics field as efforts have turned to using natural\nmaterial anisotropy in order to control material properties.\nOverall the manuscript was well written, the analysis, interpretation and conclusions\nwere largely sound. However, there are several additional major and minor points that\nshould be addressed in revisions.\nReply: We thank the referee for their positive comments on our work. We appreciate\nthe referee’s comment “the nanofabrication and investigation of arrays of\nnanostructured MoOCl2 realizing both hyperbolic localized plasmon resonances as\nwell as chiral optical responses”, which has captured the central idea of our work. We\nalso thank the referee for their helpful suggestions and revision points.\nMajor Points:\nComment 1.1. The authors should address what benefits the twisted MoOCl2 provides\nover chiral noble metal nanostructures.\nReply to 1.1: We thank the referee for the very helpful comments. The chirality of\ntwisted MoOCl nanostructures originates from natural material anisotropy, rather than\n2\nstructural anisotropy. This provides much convenience for nanofabrication and\nflexibility for structural design. In conventional noble metal (Au, Ag) nanostructures,\nasymmetric structures such as nanorods, open-angle disks or rings, are designed as\nbasic elements to achieve chirality. Twisted structures are expected to produce a strong\nchiral response, and such asymmetric structural elements are also required to design\nnoble metal twisted bilayers, to create anisotropy between the upper and lower layers\n(npj Nanophoton. 1, 20 (2024); Nat. Commun. 3, 870 (2012); Nat. Commun. 15, 9804\n(2024)). Nanofabricating twisted noble metal nanostructures is very challenging. It\nrelies on the precise alignment of upper and lower asymmetric structures, such as rods\n1\nwith twist angles. A gap layer between the upper and lower structures is also required\nto avoid mode mixing and structural collapse.\nIn contrast, our design of twisted MoOCl metasurface has a great advantage in\n2\nnanofabrication by avoiding the alignment of nanostructures and the use of a dielectric\ngap layer. This advantage originates from the material anisotropy and the Z-gap\nindependence of MoOCl modes. We believe that our design of twisted MoOCl\n2 2\nmetasurface will be more feasible for applications due to its more robust\nnanofabrication and lower cost.\nChanges in the manuscript in answer to Comment 1.1: We have added the above\ndiscussion to the revised Supplementary Information (see SI pages 17-18).\nComment 1.2. The authors should be careful to note that in a biaxial medium there are\nalways two propagating wave solutions (both extraordinary). The hyperbolic modes\noccur for only one root of the quartic wave equation. Do both roots play a role in the\nobserved modes in the H-LPRs? (see Narimanov, E. E. Phys. Rev. A 98, 013818 (2018))\nReply to 1.2: The detailed theoretical analysis of the modes supported by MoOCl bulk\n2\nand thin film can be found in literature published recently (Nat. Commun. 15, 9727\n(2024); Nat. Commun. 16, 6172 (2025); Phys. Rev. B, 100, 235408 (2019); Nano Lett.\n25, 15534-15541 (2025)). Here, we summarize the main mode types involved in the\nanalysis: (1) hyperbolic mode, (2) ghost mode, (3) lenticular mode, (4) air mode.\nFor bulk MoOCl , the hyperbolic and ghost modes are described in the following\n2\nliterature: Figure 1f, Figure 2 and Supplementary Figure 4-9 of Nat. Commun. 15, 9727\n(2024). The key feature of hyperbolic mode is a 3D hyperbolic IFC in both the in-plane\nand out-of-plane directions. The key feature of ghost mode is a cross-shaped dispersion\nin the in-plane direction only.\nFor thin film MoOCl , the hyperbolic and lenticular modes are discussed in the\n2\nfollowing literature: Figure 3 of Nat. Commun. 15, 9727 (2024) and Supplementary\nFigure 6-7 of Nat. Commun. 16, 6172 (2025). The hyperbolic mode exhibits hyperbolic\nIFC in the in-plane direction and a zigzag ray-like propagation in the out-of-plane\ndirection. The lenticular mode is another solution in the theoretical model; however,\nit’s completely different from the hyperbolic mode. The lenticular mode is a waveguide\nmode, which is polarization-selective and can only be efficiently excited with y-\npolarization. In contrast, the hyperbolic mode can be efficiently excited with x-\npolarization. In experiments, the hyperbolic mode has been well-demonstrated in both\nreal and k spaces. In real space, the hyperbolic wavefront under normal incidence and\nthe ray-like pattern under oblique incidence have been clearly observed. The measured\nopen angles of hyperbolas were in good agreement with the theoretical calculations\n(Nat. Commun. 16, 6172 (2025); Nano Lett. 25, 15534-15541 (2025)). Additionally,\nthe lenticular mode was only noticeably observed under y-polarization at short\nwavelengths (e.g. <700 nm). The ghost mode was not observed in the experiments,\npossibly due to its high loss, which makes its contribution to the total fields very weak.\n0\nair/MoOCl interface. The air mode is an influential factor in experiments, but it is not\n2\nimportant to discuss here.\nAs for the question and the literature raised by you, the “another root of the quartic\nwave equation” may refer to the lenticular mode mentioned above. As discussed above,\nunder x-polarization, only the hyperbolic mode can be efficiently excited, whereas the\nlenticular mode cannot be efficiently excited due to polarization selectivity. In addition,\nwe also wanted to point out that, under y-polarization, a dielectric resonance mode will\nemerge for a MoOCl nanostructure with a large volume size, which is still under\n2\ninvestigation and will be published as a new work in the future.\nChanges in the manuscript in answer to Comment 1.2: The revised contents in the\nSupplementary Information are as follows (see SI pages 1-2):\n“The detailed theoretical analysis of the modes supported by MoOCl bulk and thin\n2\nfilm can be found in literature published recently1-4. Here, we summarize the main mode\ntypes involved in the analysis: (1) hyperbolic mode, (2) ghost mode, (3) lenticular mode,\n(4) air mode.\nFor bulk MoOCl , the hyperbolic and ghost modes are described in the following\n2\nliterature: Figure 1f, Figure 2 and Supplementary Figure 4-9 of Nat. Commun. 15, 9727\n(2024)1. The key feature of hyperbolic mode is a 3D hyperbolic IFC in both the in-plane\nand out-of-plane directions. The key feature of ghost mode is a cross-shaped dispersion\nin the in-plane direction only.\nFor thin film MoOCl , the hyperbolic and lenticular modes are discussed in the\n2\nliterature: Figure 3 of Nat. Commun. 15, 9727 (2024)1 and Supplementary\nFigure 6-7 of Nat. Commun. 16, 6172 (2025)3. The hyperbolic mode exhibits\nhyperbolic IFC in the in-plane direction and a zigzag ray-like propagation in the out-\nof-plane direction. The lenticular mode is another solution in the theoretical model;\nhowever, it’s completely different from the hyperbolic mode. The lenticular mode is a\nwaveguide mode, which is polarization-selective and can only be efficiently excited\nwith y-polarization. In contrast, the hyperbolic mode can be efficiently excited with x-\npolarization. In experiments, the hyperbolic mode has been well-demonstrated in both\nreal and k spaces. In real space, the hyperbolic wavefront under normal incidence and\nthe ray-like pattern under oblique incidence have been clearly observed. The measured\nopen angles of hyperbolas were in good agreement with the theoretical calculations3,4.\nAdditionally, the lenticular mode was only noticeably observed under y-polarization at\nshort wavelengths (e.g. <700 nm). The ghost mode was not observed in the experiments,\npossibly due to its high loss, which makes its contribution to the total fields very weak.\nIn addition, the air mode (k =1) is a spherical wave propagating in air and near the\n0\nair/MoOCl interface. The air mode is an influential factor in experiments, but it is not\n2\nimportant to discuss here.\nAs discussed above, under x-polarization, only the hyperbolic mode can be efficiently\nexcited, whereas the lenticular mode cannot be efficiently excited due to polarization\nselectivity.”\nwavevectors are oriented along the asymptotes of the hyperbola, and their directions\nare determined by the open angle of the hyperbola.”\nThese ray-like modes seem to be attributed to “ghost modes” elsewhere. See Narimanov,\nE. E. Phys. Rev. A 98, 013818 (2018) and Venturi et al. Such directional ghost modes\nshow the unique character of having both propagating and evanescent character even\nwithout intrinsic material losses. Are the rays observed here due to the hyperbolic\nmodes (defined by the hyperbolic isofrequency surface) or the ghost modes? I don't\ndisagree that that these appear to be localized plasmon resonances in a hyperbolic\nmaterial, the question becomes do they have truly hyperbolic dispersion or not.\nReply to 1.3: As discussed in Comment1.2, in bulk MoOCl , the ghost mode has a cross-\n2\nshaped dispersion in the in-plane direction. In contrast, the hyperbolic mode exhibits\n3D hyperbolic dispersion in both the in-plane and out-of-plane directions. It exhibits a\nhyperbolic IFC in the in-plane direction and a zigzag ray-like propagation in the out-\nof-plane direction. In our case, as shown in Figure 1f, the mode profile in the x-z plane\nshows a zigzag ray-like distribution that can only be explained by the hyperbolic mode.\nThis result is also consistent with the work of Venturi et al (Figure 3 of Nat. Commun.\n15, 9727 (2024)). In the x-y plane, the hyperbolic mode can result in a ray-like mode\nas well, as demonstrated in the following literature: Nat. Commun. 15, 9727 (2024);\nNat. Commun. 16, 6172 (2025); Nano Lett. 25, 15534-15541 (2025). These references\nare also mentioned in Comment1.2. In contrast, the ghost mode was not clearly\nobserved in the experiments, possibly due to the high loss of this mode. However, we\ncannot rule out its contribution, although it may be very weak. To make the expression\nmore accurate, we modified the related description in the main text and cited the\nliterature (Phys. Rev. A 98, 013818 (2018)).\nChanges in the manuscript in answer to Comment 1.3: The revised contents in the\nmain text are as follows (see page 3):\n“Ray-like lines appear because most wavevectors are oriented along the asymptotes of\nthe hyperbola, and their directions are determined by the open angle of the hyperbola.\nThese volumetric ray-like features are hallmarks of hyperbolic dispersion and sharply\ncontrast with the purely surface-confined fields of LSPRs in Au…. In addition, the\nghost mode may have a weak contribution to the in-plane mode distribution33,38,40.”\nComment 1.4. As discussed in the supplementary information increasing R redshifts\nthe spectra while increasing H blueshifts the spectra. Could the authors explain why\nincreasing H would increase the energy of the hyperbolic mode? It seems that thin\nfilm models of surface plasmonic behavior could explain this in a quite straightforward\nfashion without needing to invoke a hyperbolic mode.\nReply to 1.4: We agree with the referee that the blueshift of spectra with increasing H\n4\nis simply the behavior of localized plasmon resonance, a phenomenon that has been\nwell understood in noble metal localized plasmon resonances. Therefore, it is not a\nfeature of hyperbolic mode. In the supplementary information, we present the results of\nspectral shift versus disk radius and height, just to show how the resonance wavelength\nchanges, so that readers can directly use this data for their experiments. To avoid\nconfusion, we added some descriptions in the SI.\nChanges in the manuscript in answer to Comment 1.4: The revised contents in the\nSupplementary Information are as follows (see SI page 5):\n“The resonance wavelength redshifts with an increase in radius and blueshifts with an\nincrease in thickness, which is simply the behavior of localized plasmon resonance.\nThis behavior has been well understood in noble metal localized plasmon resonances\nand it is not a feature of hyperbolic modes.”\nMinor Points:\nComment 1.5. Figures 2d and e, please clarify more in the figure itself that the spectra\nare being plotted versus disk radius.\nReply to 1.5: We revised the figures by adding radius “R=” before disk sizes.\nComment 1.6. Figure 3 is confusing. It was hard to tell which of the subpanels were\nwhich polarizations and smaller FOVs at first glance. I would recommend modifying\nthe arrangement of the panels and perhaps being more selective on which panels are\ndisplayed in the main text.\nReply to 1.6: We modified the arrangement of the panels in Figure 3, and moved the\nPEEM images for FOV=20 μm and 10 μm to the SI as Fig. S8.\nReviewer #2 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nReviewer #3 (Remarks to the Author):\nComments about NCOMMS-25-92838-T\nIn this work, the authors report hyperbolic localized plasmon resonances in the two-\ndimensional material MoOCl2, which exhibits strong in-plane anisotropy, and\nintroduce twist-induced chirality in geometrically symmetric metasurfaces. The\nobserved plasmon resonances feature one-dimensional confinement, z-gap\nindependence, and pronounced circular dichroism arising from twist-induced chirality.\nHowever, promising hyperbolic media are expected to exhibit high electromagnetic\nconfinement, low energy loss, and flexible tunability under external fields. The\nhyperbolic MoOCl2 system does not offer any fundamentally new advantages in\nelectromagnetic confinement, energy loss and tunability, compared with previously\nreported materials such as MoO3, h-BN, WTe2, Ga2O3 and black phosphorus, all of\nwhich have already been extensively studied for supporting hyperbolic polaritons. In\naddition, the current experimental data set is incomplete and insufficient to support the\nmajor claims making it difficult to evaluate the robustness of the conclusions. As a\nresult, the novelty of this work appears limited for publication in Nature\nCommunications and would be more suitable for a specialized journal.\nReply: We thank the referee for their comments. However, we respectfully have a\ndifferent view from the referee on this point. The referee states that “The hyperbolic\nMoOCl system does not offer any fundamentally new advantages in electromagnetic\n2\nconfinement, energy loss and tunability, compared with previously reported materials\nsuch as MoO3, h-BN, WTe2, Ga2O3 and black phosphorus”, so they don’t recommend\nworks based on this material. We believe this assessment does not fully reflect the\ndistinct advantages of the MoOCl system.\n2\nas has been demonstrated in recent publications in high-ranking journals (Nat. Commun.\n15, 9727 (2024); Science 387, 786-791 (2025); Nat. Commun. 16, 6172 (2025); ACS\nNano 19, 25413-25421 (2025)). As these papers have clearly demonstrated the intrinsic\nproperties of MoOCl material and the hyperbolic plasmon polaritons supported by\n2\nimportant points. To the best of our knowledge, MoOCl is the only material reported\n2\nso far that supports hyperbolic polaritons in the visible and near-infrared range. This\nspectral range is essential for many applications, including optical communications,\ninformation processing, photocatalysis and sensing. In addition, the optical properties\nof MoOCl are excellent, showing clean metallic property along the x-axis and wide-\n2\nbandgap dielectric property along the y- and z-axes in the visible and near-infrared\nrange. To our knowledge, no previously reported material has shown this combination\nof properties. The unique optical properties of MoOCl , especially its permittivity,\n2\nmake it a unique material for nanophotonic designs of resonance modes and\nmetasurfaces, and this is the starting point of this study. Our results also demonstrate\nour contribution directly by showing three unprecedented properties:\n(i) one-dimensional resonances in circularly symmetric geometries,\n(ii) Z-gap independence in metal–insulator–metal structures, and\n(iii) twist-induced chirality without breaking geometric symmetry.\nIn addition, we agree that confinement, loss, and tunability are important, but they\nshould be evaluated in the appropriate spectral range and application context. For\nexample, MoOCl nanostructures can support localized plasmon resonances and thus\n2\nhigh electromagnetic confinement from visible to near-infrared range, none of the\nmaterials listed above can support hyperbolic-polariton electromagnetic confinement\nin this range. Finally, we would like to comment on the tunability. In nanophotonics,\nthe general approach is to design nanostructures and metasurfaces to control the light\nfield, without changing the intrinsic material properties. Regarding the material\n6\ntunability itself, MoOCl has been predicted to exhibit a strain response (Phys. Rev. B\n2\n102, 245419 (2020)), and it’s too early to conclude that it is incapable of other tunability\nat this stage, which should be studied further in the future.\nOther comments will be replied below point by point.\nComments:\nComment 3.1. The authors claim that MoOCl₂ exhibits one-dimensional characteristics\nin its hyperbolic localized plasmon resonances. However, one-dimensional materials\nare generally composed of 1D structural units connected by weak van der Waals\ninteractions, which is not clearly illustrated or discussed in Fig. 1a. Clarification on the\nstructural origin of this claimed one-dimensionality is necessary.\nReply to 3.1: The “structural origin of this claimed one-dimensionality” has been\ndiscussed in detail in previous publications (Nat. Commun. 15, 9727 (2024); Science\n387, 786-791 (2025); Nat. Commun. 16, 6172 (2025); Phys. Rev. B 102, 245419 (2020);\nPhys. Rev. B 104, 205424 (2021)), which have been cited in the manuscript.\nTo keep the present paper focused, we did not repeat the full descriptions; however,\nfollowing the referee’s suggestion, we added some descriptions to clarify this issue in\nthe revised manuscript.\nChanges in the manuscript in answer to Comment 3.1: The revised contents in the\nmain text are as follows (see page 2):\n“MoOCl is a layered van der Waals crystal with a monoclinic structure (space group\nalong the Mo–O chains, while the inter-chain coupling in the orthogonal direction is\nsignificantly weaker. Along the Mo–O chain axis, the material is metallic (ε < 0),\nx\nwhereas the orthogonal directions remain dielectric (ε , ε > 0) across the visible to\ny z\nnear-infrared spectrum (Fig. 1a,b)”.\nComment 3.2. In Fig. 1b, the real part of the permittivity appears to vary almost linearly\nwith wavelength, which seems unusual for 2D materials. It would be necessary to also\nprovide the imaginary part of the optical dielectric function, as the real and imaginary\ncomponents should satisfy the Kramers–Kronig relation. Including this information\nwould help verify the physical consistency of the presented optical data. If experimental\nmeasurements are challenging, first-principles calculations could also be provided to\nsupport and better interpret the observed results.\nReply to 3.2: The permittivity that includes both real and imaginary components over\na broad spectral range, has been reported both in experimental measurements and first-\nprinciples calculations by several groups (Science 387, 786-791 (2025); Nat.\nCommun. 16, 6172 (2025); ACS Nano 19, 25413-25421 (2025); Phys. Rev. B 102,\n245419 (2020); Phys. Rev. B 104, 205424 (2021)). These papers have also been cited\nat the corresponding positions when mentioning the permittivity of MoOCl . To keep\n2\n7\nthe present paper focused, we did not repeat the full analysis; however, following the\nreferee’s suggestion, we now provide the permittivity that includes both real and\nimaginary components in the revised SI.\nIn addition, it should be noted that the in-plane permittivity shown in Fig. 1b was\nmeasured by us previously (Nat. Commun. 16, 6172 (2025)). For a broad spectral range\nfrom the visible to mid-infrared, the following papers are good references: SI Fig. S3\nand Table S1 of Science 387, 786-791 (2025); Fig.1b of Nat. Commun. 16, 6172 (2025);\nFig. 2 of ACS Nano 19, 25413-25421 (2025).\nAs you mentioned for the permittivity along the metallic axis, “the real part of the\npermittivity appears to vary almost linearly with wavelength”, you will find that it’s\nclean metal permittivity in a broad wavelength range, which can be well fitted with\nDrude model (SI Fig. S3 and Table S1 of paper Science 387, 786-791 (2025). Several\nmonths ago, we also measured the permittivity from the visible to mid-infrared\nwavelengths, and our result is consistent with the paper above, except for slight\ndeviations in the fitting values.\nChanges in the manuscript in answer to Comment 3.2: The revised contents in the\nSupplementary Information are as follows (see SI page 2):\n“Figure S1 presents the measured in-plane permittivity, including both the real and\nimaginary components.\nFig. S1. Measured permittivity along the two orthogonal directions in the visible to near-\ninfrared range. The light red shading indicates Re(ε )<0.\nx\n”\nComment 3.3. The physical origin of the observed hyperbolicity should be clarified.\nIn particular, the respective roles of interband and intraband transitions, which are crucial\nfor producing strong optical anisotropy and hyperbolic dispersion, need to be discussed\nin greater detail. Providing this analysis would help elucidate the microscopic\nmechanism underlying the reported hyperbolic behavior. Similar discussions has been\nreported in Nat Commun 11, 1158 (2020).\nReply to 3.3: The hyperbolic property originates from the anisotropic permittivity\n8\ncomponents of opposite signs of a material. The anisotropic permittivity originates from\nthe special band structure of the material. As mentioned in above Comments, the\npermittivity and band structure of MoOCl have been investigated through first-\n2\nprinciples calculations and experiments, where the roles of interband and intraband\ntransitions were also discussed (Science 387, 786-791 (2025); Phys. Rev. B 102,\n245419 (2020); Phys. Rev. B 104, 205424 (2021)). We also have a short discussion on\nthis issue in our previous work: “The enhanced absorption at shorter wavelengths\noriginates from the d-band excitation in Au, whereas the case in MoOCl is more\n2\ncomplex, involving the total contribution of eight bands near the Fermi level, mainly\nfrom the 4d orbitals of Mo atoms” (Nat. Commun. 16, 6172 (2025).\nTo keep the present paper focused, we did not repeat the full analysis; however,\nfollowing the referee’s suggestion, we added some discussions in the SI and cited the\npaper mentioned by the referee in the main text as a new Ref.30.\nIt should be noted that the central point of our manuscript is the nanofabrication and\ninvestigation of nanostructured MoOCl metasurfaces to realize hyperbolic localized\n2\nplasmon resonances and produce a new tool for nanophotonics in the visible and near-\ninfrared range.\nChanges in the manuscript in answer to Comment 3.3: The revised contents in the\nSupplementary Information are as follows (see SI pages 2-3):\n“The hyperbolic property originates from the anisotropic permittivity components of\nopposite signs of a material. The anisotropic permittivity originates from the special\nband structure of the material. The permittivity and band structure of MoOCl have\n2\nbeen investigated through first-principles calculations and experiments, where the roles\nof interband and intraband transitions were also discussed5-7. Here we summarize the\nkey points. MoOCl belongs to the oxychloride family of van der Waals materials,\n2\nwhich is generally characterized by weak interlayer coupling and lattice distortions,\nenabling exotic anisotropic physics. In the case of MoOCl , an orbital-selective Peierls\n2\ndistortion produces one-dimensional dimerized Mo chains, rendering Mo-dxy bands\nessentially dispersion less and splitting them away from the Fermi surface, whereas\ndxz/yz bands disperse through the Fermi level but with strong in-plane anisotropy.\nMoOCl exhibits metallic electronic band structures with abundant electronic states at\n2\nthe Fermi level and thus intrinsic high carrier density, which facilitates the generation\nof high-frequency plasmons. The four bands across the Fermi level exhibit pronounced\nanisotropy. Along the Γ-X direction, the bands are highly dispersive, whereas along the\nΓ-Y direction, they are relatively flattened. The eight bands across and near the Fermi\nlevel are mainly contributed by the 4d orbitals of Mo atoms with different spatial\nsymmetries, which are, respectively, the dz2 orbitals, the dxz orbitals, the dxy orbitals,\nand the dyz orbitals. The Bloch electron wave functions of the eight bands at the Γ point\nalso verify the anisotropic features. Such anisotropic electronic states dominate the\nanisotropic plasmonic response of MoOCl . Computational studies have suggested that\n2\nthis electronic structure gives MoOCl optical hyperbolicity with interband transitions\n2\npushed to higher energies, enabling HPPs. The hyperbolic band extends to visible\n9\nfrequencies. Moreover, interband transitions do not appear until photon energy >2.5 eV,\nso that dielectric losses from interband transitions are suppressed within the hyperbolic\nband, enabling low-loss propagation of HPPs.”\nComment 3.4. The presented hyperbolic isofrequency contours appear incomplete.\nAdditional data points at a wider range of frequencies should be included to clearly\nillustrate the frequency range over which hyperbolicity occurs, as well as the transition\nfrom elliptic to hyperbolic dispersion. This would provide a more comprehensive\nunderstanding of the material's optical anisotropy and dispersion characteristics.\nReply to 3.4: The hyperbolic isofrequency contours for MoOCl thin films and the\n2\npermittivity at wide range of frequencies have been well reported in previous papers\n(Nat. Commun. 15, 9727 (2024); Science 387, 786-791 (2025); Nat. Commun. 16,\n6172 (2025); Phys. Rev. B 102, 245419 (2020);Phys. Rev. B 104, 205424 (2021)). For\nexample: In Nat. Commun. 16, 6172 (2025), the “frequency range over which\nhyperbolicity occurs, as well as the transition from elliptic to hyperbolic dispersion”\nwere presented in Fig.1b, Supplementary Figure 5 and Supplementary Figure 7. Similar\nresults can also be found in the other two papers (Nat. Commun. 15, 9727 (2024);\nScience 387, 786-791 (2025)).\nTo keep the present paper focused, we did not repeat the full analysis; however,\nfollowing the referee’s suggestion, we now summarize some key features in the SI for\ncompleteness.\nChanges in the manuscript in answer to Comment 3.4: The revised contents in the\nSupplementary Information are as follows (see SI page 2):\n“As indicated by the permittivity curves in Fig. S1, Re(ε ) = 0 occurs at the wavelength\nx\nof approximately . Therefore, hyperbolic range is from λ to longer\ntran\nwavelength (e.g., near-infrared), and elliptical range is from λ to shorter wavelength\ntran\n𝜆𝑡𝑟𝑎𝑛 = 525 nm\n(e.g., 450 nm). It should be noted the Re(ε ) <0 when the wavelength reaches mid-\ny\ninfrared (~4.0 ), where the in-plane IFCs will become elliptical again. Therefore,\nthe hyperbolic dispersion will persist in part of the visible range and the full broad near-\n𝜇𝑚\ninfrared range.”\nComment 3.5. The wavelength ratio of the hyperbolic in-plane dispersion to the\ncorresponding free-space photon wavelength (i.e., electromagnetic confinement)\nshould be provided, along with the propagation length and lifetime of the hyperbolic\npolaritons. These parameters are essential for quantitatively evaluating the performance\nand quality of hyperbolic materials.\nReply to 3.5: These properties have been systematically characterized in previous\nworks (Nat. Commun. 15, 9727 (2024); Science 387, 786-791 (2025); Nat.\nCommun. 16, 6172 (2025); Nano Lett. 25, 15534-15541 (2025)).\nFor examples:\nspace photon wavelength” corresponds to the dispersion relation in previous papers,\nsee Fig. 4 of Nat. Commun. 15, 9727 (2024), Fig. 4 of Science 387, 786-791 (2025),\nand Supplementary Figure 8 of Nat. Commun. 16, 6172 (2025).\n“The propagation length and lifetime of the hyperbolic polaritons” was provided in Fig.\n4 of Nat. Commun. 15, 9727 (2024), Fig. 2 of Science 387, 786-791 (2025), Fig. 4 and\nFig. S9 of Nano Lett. 25, 15534-15541 (2025).\nFor your convenience, a selected paragraph from Nano Lett. 25, 15534-15541 (2025)\nis provided below:\n“A key property of hyperbolic plasmon polaritons for prospective on-chip applications\nin the visible to near-infrared range is their lifetime. To measure it, we extracted the\namplitude line profile of the edge-launched fringes along the x-direction at a\nrepresentative wavelength of 1000 nm (Figure 4a, c) (see Note S9, Supplementary\nInformation for PEEM image with tunable wavelengths). The hyperbolic mode\ncomponents are extracted through the high-pass filter (See details of data processing in\nNote S10 in the Supporting Information) and fitted it with an exponentially decaying\nsinusoidal function (Figure 4b, d).\n2𝑥\n−𝐿𝑥\n𝐴𝑒 sin[(𝑘𝑜𝑏𝑠 −∆𝑘)𝑥−𝜑]\nFig. 4. Observation and analysis of edge-launched hyperbolic modes. (a, c) PEEM image\nof fringes excited by etched orthogonal lines at oblique incidence and normal incidence,\nrespectively. The thickness of this MoOCl flake is ~64 nm, and the wavelength is 1000 nm.\n2\n(b, d)The fringes of hyperbolic mode components extracted from PEEM images along\n11\nthe x-direction marked in (a, c) (blue dots). The damped sine-wave function (black solid\nline) was fitted to the data that corresponded to edge-launched fringes.\nBased on the fitting parameters, the amplitude decay lengths\nand are obtained for oblique and normal incidence,\n𝐿𝑥 = 5.56±0.566 𝜇𝑚\nrespectively. These values are approximately several times the incident light\n𝐿𝑥 = 5.94±0.544 𝜇𝑚\nwavelength in free space (5~6 ). The calculated quality factors (Q-factor), given by\n, reach ~9.14 and ~9.98 in MoOCl hyperbolic plasmon polaritons\n2\n𝜆0\nwith oblique and normal incidence, respectively. The lifetime can be further obtained\n𝑄 = 𝑅𝑒(𝑘)/𝐼𝑚(𝑘)\naccording to , where the group velocity is taken from the\ndispersion relation (see more details in Note S11 in the Supporting Information). For\n𝜏𝑥 = 𝐿𝑥/𝑣𝑔 𝑣𝑔 = 𝑑𝜔/𝑑𝑘\nthe in-plane hyperbolic plasmon polaritons in MoOCl , we obtain the lifetimes are\n2\nand , which are an order of magnitude larger\nthan the period of free-space light .”\n𝜏𝑥 = 54.5±5.55 fs 𝜏𝑥 = 58.2±5.33 fs\n𝑇0 = 3.33 fs\nIn general, the wavelength compression is not as high as that of phonon polaritons in\nthe mid-infrared range. This is reasonable considering the plasmonic properties of\nMoOCl in the visible and near-infrared range. And in our study, we didn’t use the film\n2\nitself to confine electromagnetic field, instead, we use nanostructures. This is the\nmeaning of making nanostructures, which produce much stronger field confinement\nand near-field enhancement than unpatterned films.\nIn addition, the propagation length is about several micrometers, and the lifetime is\naround 60 fs for a MoOCl film.\nfollowing the referee’s suggestion, we now summarize the key parameters in the SI and\nFig. S2 for completeness.\nChanges in the manuscript in answer to Comment 3.5: The revised contents in the\nSupplementary Information are as follows (see SI pages 3-4):\n“Figure S2 presents the dispersion relation of hyperbolic polaritons supported by a ~60\nnm MoOCl film3,4. At a representative excitation wavelength of 1000 nm, the\n2\ncorresponding effective wavelength of the hyperbolic polariton ( ) is 615 nm, that\nis 1.63k . The propagation of hyperbolic mode is fitted with an exponentially decaying\n0\n𝜆𝐻𝑃𝑃𝑠\nsinusoidal function . The propagation length (Lx=1/Im(q))\nis approximately 5.94−𝐼𝑚(𝑞, )𝑥which is approximately six times the incident light\n𝐴𝑒 sin[𝑅𝑒(𝑞)𝑥−𝜑]\nwavelength in free space (~6 ). The lifetime ( ) is approximately 58.2 fs, calculated\n𝜇𝑚\nby , where the group velocity is taken from the dispersion\n𝜆0 𝜏\nrelation. The lifetime is an order of magnitude larger than the period of free-space light\n𝜏 = 𝐿𝑥/𝑣𝑔 𝑣𝑔 = 𝑑𝜔/𝑑𝑘\n. The calculated quality factor (Q factor) defined by\nreaches ~10. It should be noted that this definition of Q factor is not a standard and\n𝑇0 = 3.33 𝑓𝑠 𝑄 = 𝐿𝑥/𝜆𝐻𝑃𝑃𝑠\nuniversal form for cavities. According to the standard definition, the Q factor is related\nto the lifetime by , where fs-1 is the angular frequency of the\nexcitation light at nm. The standard Q factor is calculated to be ~110.\n𝑄 = 𝜔0𝜏 𝜔0 = 1.884\n12\n𝜆0 = 1000\nUsing the standard definition of Q factor will be convenient for comparison with the Q\nfactor of H-LPRs supported by a MoOCl metasurface. In that case, .\n2\n𝑄 = 𝜔0𝜏 = 𝜆0⁄Δ𝜆\nFig. S2. Calculated polariton dispersion relation by transfer matrix method. The red dots denote\nexperimental results of ~60 nm MoOCl flake excited with x-polarizations at normal incidence.\n0\n”\n𝑘 = 2𝜋/𝜆\nComment 3.6. Plasmon hyperbolic materials often exhibit higher losses, a short\ndiscussion on loss mechanisms in MoOCl2, including thickness dependence and Q-\nfactor of H-LPRs would help readers assess performance limits and potential device\nimplications.\nReply to 3.6: The loss of material itself is correlated with the imaginary part of\npermittivity, which behaves as the absorption of the material, involving interband and\nintraband transitions. For nanostructures, except for absorption loss, radiative decay\n(also called scattering decay) is another pathway. That is to say, the decay pathway of\nlocalized plasmons supported by MoOCl nanostructures includes both absorption loss\n2\nand radiative decay. The former depends on the material itself; the latter depends on\nthe design of the nanostructures, including their geometric size and shape, the\nmetasurface period and the dielectric environment (J. Chem. Phys. 153, 120902 (2020);\nPhys. Rev. Lett. 124, 163901 (2020)). For example, the radiative decay rate is positively\ncorrelated with geometric size, including the thickness of the nanostructures. The total\ndecay rate can be characterized by the Q factor or linewidth, obtained from the\ntransmission or reflection spectra. As shown in Fig. 4d of the main text, the Q factor\nfor the MoOCl metasurface is calculated to be , which is much\n2\nsmaller than the Q factor (~110) for propagating hyperbolic polaritons on MoOCl film\n2\n𝑄 = 𝜆0⁄∆𝜆 = 7.2\ncalculated in Comment 3.5. The loss pathway of propagating hyperbolic polaritons\nsupported by a MoOCl film is mainly determined by material absorption. And the\n2\nabsorption loss then determines the upper limit of the Q factor of a nanostructure.\nThe small Q factor for the MoOCl metasurface indicates that radiative decay plays a more\n2\nsignificant role than absorption loss, which is consistent with previous reports on Au\nnanostructures (Phys. Rev. Lett. 124, 163901 (2020)). It should be noted that\nradiative decay can be further suppressed by designing the structural parameters and\nintroducing mode coupling and interference.\nSupplementary Information are as follows (see SI page 4):\n“The decay pathway of localized plasmons supported by MoOCl nanostructures\n2\nincludes both absorption loss and radiative decay. The former depends on the material\nitself; the latter depends on the design of the nanostructures, including their geometric\nsize and shape, the metasurface period and the dielectric environment9,10. For example,\nthe radiative decay rate is positively correlated with geometric size, including the\nthickness of the nanostructures. The total decay rate can be characterized by the Q factor\nor linewidth, obtained from the transmission or reflection spectra. As shown in Fig. 4d\nof the main text, the Q factor for the MoOCl metasurface is calculated to be\n2\n, which is much smaller than the Q factor (~110) for propagating\n𝑄 =\nhyperbolic polaritons on MoOCl film calculated above. The loss pathway of\n2\n𝜆0⁄∆𝜆 = 7.2\npropagating hyperbolic polaritons supported by a MoOCl film is mainly determined\n2\nby material absorption. And the absorption loss then determines the upper limit of the\nQ factor of a nanostructure. The small Q factor for the MoOCl metasurface indicates\n2\nthat radiative decay plays a more significant role than absorption loss, which is\nconsistent with previous reports on Au nanostructures10. It should be noted that\nradiative decay can be further suppressed by designing the structural parameters and\nintroducing mode coupling and interference.”\nComment 3.7. The manuscript states that chirality is robust to thickness mismatch and\nfabrication variations, but it would help to quantify the tolerance (percent-level\ndeviations in thickness or twist angle).\nReply to 3.7: To address the referee’s comment, we added a new Figure in the SI to\nfurther demonstrate the robustness of chirality to deviations in twist angle and thickness.\nChanges in the manuscript in answer to Comment 3.7: The revised contents in the\nSupplementary Information are as follows (see SI page 13):\n“The chirality is robust to thickness mismatch and fabrication variations, as shown in\nFig. S15.\nFig. S15. Robustness of chirality to deviations in twist angle and thickness. (a) Extreme\nvalues of CD versus twist angle, using the structural parameters in Fig. S11. (b) Extreme values\n14\nof CD versus thickness deviation, using the structural parameters in Fig. S14e.\nComment 3.8. Can the authors elaborate on the microscopic origin of the twist-induced\nchirality, possibly through a brief tensor-transformation argument for the rotated\npermittivity?\nReply to 3.8: As previously discussed in the SI, “More precise numerical calculations\nand theoretical analyses should be conducted by theoretical groups elsewhere. As an\nexperimental study, our primary concern lies in the experimental demonstration of the\nnew concepts and ideas.” Several aspects should be considered when building an\nanalytical model. These include, but are not limited to, the rotated permittivity tensor,\npropagation and geometric phases, the different resonance wavelengths of the upper\nand lower disks, and the near-field mode distributions under different polarization states.\nWe believe there will be theoretical groups who are interested in building analytical\nmodels. For example, last month in a conference, we found some groups who are trying\nto build analytical models of twisted Au nanorods.\nIn our current study, we have demonstrated the features of twist chirality supported by\nMoOCl in both experiments and FDTD simulations. And the twist chirality can be\n2\nunderstood by breaking the symmetry of the permittivity axis. We believe this is\nsufficient for the current stage.\nComment 3.9. Would chirality persist in multilayer twist stacks (beyond bilayers),\nand if so, does the effective thickness model remain applicable?\nReply to 3.9: The chirality will persist in multilayer twist stacks. For example, in three-\nlayer structures, the top layer has a twist angle of θ relative to the bottom layer, while\nthe middle layer has a twist angle of θ/2 relative to the bottom layer. The chirality will\npersist because the middle layer can be regarded as a gradient transition layer between\nthe top and bottom layers. In this case, the chirality can also be understood from the\neffective thickness model, but the situation is more complex.\nBelow is a simulation result for twisted three layers.\nChanges in the manuscript in answer to Comment 3.9: The revised contents in the\nSupplementary Information are as follows (see SI page 13):\n“The chirality persists in twisted multilayer stacks, as shown in Fig. S16.\n2\n( , , twist angle between top and bottom layers is 60°, and the\ntwist angle between middle and bottom layers is 30°).\n𝑅 = 100 nm 𝐻 = 70 nm\nReviewer #4 (Remarks to the Author):\nThis manuscript reports the discovery and experimental demonstration of the\nhyperbolic localized plasmon resonances (H-LPRs) in the anisotropic two-dimensional\nvan der Waals material MoOCl₂. H-LPRs originate from the intrinsic in-plane\nanisotropic permittivity (metallic along the Mo-O chain axis, dielectric in orthogonal\ndirections), leading to hyperbolic iso-frequency contours. H-LPRs exhibit three\nimportant properties: one-dimensional resonance, Z-gap independence and twist-\ninduced chirality. These properties are validated through far-field spectroscopy, near-\nfield photoemission electron microscopy imaging, and comprehensive simulations.\nOverall, the manuscript is clearly written and the topic is of interest. However, prior to\npublication, several issues should be addressed:\nReply: We thank the referee for their positive comments on our work. We also thank\nthe referee for their helpful suggestions and revision points.\nComment 4.1. The authors attribute Z-gap independence to the matching permittivity\nbetween MoOCl₂ and Al₂O₃. Could a more quantitative analysis be provided to explain\nwhy the high-k gap modes is strongly suppressed, leading to insensitivity to gap\nthickness?\nReply to 4.1: In our understanding, the high-k gap mode is mainly correlated with the\nz-axis permittivity. The z-axis permittivity of MoOCl behaves as a dielectric, with its\n2\nvalue close to that of Al O . There is no sharp permittivity transition in the gap along\n2 3\nthe z-axis direction, thus the high-k gap mode is strongly suppressed. To demonstrate\nthis point, we performed some FDTD simulations by replacing the z-axis permittivity\n(ε ) of MoOCl with its metallic x-axis permittivity (ε ). As shown in Fig. S10, the gap\nz 2 x\nmode emerges when ε is replaced by ε .\nz x\nIn conventional noble metal (Au, Ag) LSPRs, such a case has not been considered or\n16\nanalyzed, because these noble metals are isotropic. This may be one reason why, to our\nknowledge, the importance of the permittivity along the z-axis has not been explicitly\nanalyzed in previous works.\nThe permittivity of material is crucial for nanophotonics, including its sign and value.\nEven a moderate change in the permittivity can result in a significantly different\nnanophotonic mode. Therefore, exploring novel natural materials with unusual\npermittivity will be an important research frontier for future nanophotonics.\nWe believe that the novel material, MoOCl , will inspire new design ideas and special\n2\napplications in nanophotonics.\nChanges in the manuscript in answer to Comment 4.1: The revised contents in the\nSupplementary Information are as follows (see SI page 9):\n“In our understanding, the high-k gap mode is mainly correlated with the z-axis\npermittivity. The z-axis permittivity of MoOCl behaves as a dielectric, with its value\n2\nclose to that of Al O . There is no sharp permittivity transition in the gap along the z-\n2 3\naxis direction, thus the high-k gap mode is strongly suppressed. To demonstrate this\npoint, we performed some FDTD simulations by replacing the z-axis permittivity (ε )\nz\nof MoOCl with its metallic x-axis permittivity (ε ). As shown in Fig. S10, the gap\n2 x\nmode emerges when ε is replaced by ε .\nz x\nIn conventional noble metal (Au, Ag) LSPRs, such a case has not been considered or\nanalyzed, because these noble metals are isotropic. This may be one reason why, to our\nknowledge, the importance of the permittivity along the z-axis has not been explicitly\nanalyzed in previous works.\nFig. S10.Gap mode versus z-axis permittivity. (a) Simulated reflection spectra for the MIM\nstructures with gap sizes of 0–20 nm at x-polarization. The z-axis permittivity (ε ) of MoOCl\nz 2\nis replaced by its metallic x-axis permittivity (ε ). The permittivity values in the other axes\nx\nremain unchanged. The structural parameters are the same as those in Fig. 4e of the main text.\n(b) Simulated reflection spectrum of the MIM structures with a gap size of 10 nm at x-\npolarization. The resonance peak at 1300 nm is attributed to the gap mode. (c) Corresponding\nelectric field distribution (|E|) of the gap mode in the x–z plane.\nThe permittivity of material is crucial for nanophotonics, including its sign and value.\nEven a moderate change in the permittivity can result in a significantly different\nnanophotonic mode. Therefore, exploring novel natural materials with unusual\npermittivity will be an important research frontier for future nanophotonics.\nWe believe that the novel material, MoOCl , will inspire new design ideas and special\n2\napplications in nanophotonics.”\nComment 4.2. For anisotropic 2D materials (e.g., α-MoO₃), studies have shown that\nsignificant circular dichroism can be achieved by directly stacking two flakes with a\ntwist angle. If two pristine, unpatterned MoOCl₂ flakes are stacked with a twist, what\nwould be the expected CD value of such a system? Is fabricating a metasurface to obtain\nH-LPRs a necessary condition for achieving the strong chirality?\nReply to 4.2: Yes, the circular dichroism can be achieved by directly stacking MoOCl\n2\nflakes with a twist angle. Indeed, we also provided our experimental data for\nunpatterned MoOCl flakes as references in our manuscript, as shown in Fig. S17a and\nchiral responses for unpatterned MoOCl , but there are no resonance peaks like those\n2\nof MoOCl metasurfaces. In addition, the transmittance of unpatterned MoOCl is much\n2 2\nlower than that of MoOCl metasurfaces.\ntwist angles, as shown in Fig. S22. The film thickness is the same as that of Fig. S11.\nAs we can see, the chiral responses are weaker than those of the metasurfaces, and the\nCD values are always below zero within a wide spectral range (Fig. S22b).\nIt should be noted that the advantages of the metasurface are not simply for achieving\nstrong chirality. More importantly, the localized plasmons support localized near-field\nenhancements, which are much stronger than those of unpatterned films. Such near-\nfield enhancements can largely enhance light-matter interaction, which is beneficial for\nchiral sensing and detection. In addition, the metasurface exhibits clear resonance peaks,\nwhich are also advantageous for applications.\nChanges in the manuscript in answer to Comment 4.2: The revised contents in the\nSupplementary Information are as follows (see SI page 18):\n“We also provided our experimental data for unpatterned MoOCl flakes as references,\n2\nas shown in Fig. S17a and Fig. S19b of SI (labeled by plane-LCP and plane-RCP). As\nwe can see, there are still chiral responses for unpatterned MoOCl , but there are no\n2\nresonance peaks like those of MoOCl metasurfaces. In addition, the transmittance of\n2\nunpatterned MoOCl is much lower than that of MoOCl metasurfaces.\n2 2\nFurthermore, we compared the circular dichroism in FDTD simulations at different\ntwist angles, as shown in Fig. S22. The film thickness is the same as that of Fig. S11.\nAs we can see, the chiral responses are weaker than those of the metasurfaces, and the\nCD values are always below zero within a wide spectral range (Fig. S22b).\n2\ntransmission spectra of LCP and RCP light at twist angles of 0–180° ( ). (b)\nSimulated transmission spectra and calculated circular dichroism (CD) at a twist angle of\n𝐻1 = 𝐻2 = 100 nm\n.\n𝜃 =\n”\n55°\nComment 4.3. To demonstrate hyperbolic properties, the inset in Fig. 1b only\nemphasizes the hyperbolic in-plane isofrequency contours (xy-plane). However, in Fig.\n1f, the ray-like electric field distribution, which is a hallmark of hyperbolicity, appears\nto be stronger out-of-plane (xz-plane). Does this suggest that the one-dimensional\nresonance characteristic stems from both in-plane and out-of-plane hyperbolic\nproperties?\nReply to 4.3: Yes, you are right. The full 3D isofrequency contours can be found in the\nliterature: Fig. 1f of Nat. Commun. 15, 9727 (2024), showing an open-angle 3D\nhyperboloid. The cross sections in both in-plane and out-of-plane are hyperbolas. Here,\nin the inset of Fig.1b, we plotted only the x-y plane for simplicity, to make it easier for\nreaders unfamiliar with this field to understand.\nChanges in the manuscript in answer to Comment 4.3: The revised contents in the\nmain text are as follows (see page 3):\n“It should be noted that the full 3D IFCs can be found in the literature33, showing an\nopen-angle 3D hyperboloid.”\nComment 4.4. Lines 78-80 of the manuscript state: \"These volumetric ray-like features\nare...sharply contrast with the purely surface-confined fields of LSPRs in Au.\" For a\nmore intuitive and direct comparison, it would be helpful to provide simulated electric\nfield distributions for Au LSPRs.\nReply to 4.4: Following your suggestion, we included the simulated electric field\ndistributions for Au LSPRs in the revised SI.\nSupplementary Information are as follows (see SI page 5):\n“Figure S3 presents the simulated electric field distributions for Au LSPRs for\ncomparison with those of MoOCl .\nparameters and profile positions are the same as the MoOCl disk in Fig. 1f of the main text.\n2\n”\nComment 4.5. In the introduction, when discussing hyperbolic polaritons, the reviewer\nrecommends citing Nature Communications 11, 1158 (2020), which reports WTe₂ as\nanother hyperbolic material and is relevant to the context.\nReply to 4.5: Following your suggestion, we cited this paper in the revised main text as\na new Ref.30.\nReviewer #1 (Remarks to the Author):\nThe manuscript by Li et al. describes the nanofabrication and investigation of arrays of\nnanostructured MoOCl2 realizing both hyperbolic localized plasmon resonances and\nchiroptical responses. The authors have address my major concerns regarding the\nmanuscript, however, some of the revisions have been added only to the supplementary\ninformation with minimal effort to improve the descriptions and narrative of the main\nmanuscript. I would recommend that the authors consider what portions of the\nexplanations added to the supplementary information can be added to the main text of\nthe manuscript. After such a minor improvement in the readability of the manuscript I\nrecommend that it is published in Nature Communications.\nReply: We thank the reviewer for accepting our manuscript. We have checked the\nreviewers’ comments. According to our evaluation, it would be better to remain at the\ncurrent stage. The main text is fluent, and readers can easily find more details in the SI\nif needed. Incorporating too many details into the main text would make it overly\nverbose.\nReviewer #2 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nReviewer #3 (Remarks to the Author):\nThe authors have carefully and thoroughly addressed the majority of the reviewers'\ncomments. The responses are detailed, and the revised manuscript reflects substantial\neffort in clarifying the methodology, improving the presentation, and correcting the\nissues raised. Most concerns have been adequately resolved, with corresponding\nrevisions implemented throughout the manuscript. Nevertheless, it should be noted that\nthe overall level of innovation remains limited. The main contributions are largely built\nupon previously published studies, and the revisions primarily focus on clarification.\nThat said, in view of the authors's serious and constructive attitude, the completeness\nof their responses, and the overall improvements made in the revised version, the\nmanuscript now meets the basic standards for publication in this journal. I therefore\nrecommend acceptance of the manuscript in its current form.\nReply: We thank the reviewer for accepting our manuscript.\nReviewer #4 (Remarks to the Author):\nThe authors have carefully addressed the reviewer’s concerns. Therefore, the reviewer\nrecommends the manuscript for publication at this stage.\nReply: We thank the reviewer for accepting our manuscript.\n1"}]

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