Harnessing Van Hove singularities for terahertz photoresponse via Fermi surface reconstruction in kagome lattices

Domain: physics
Published: 2026-01-22
Editorial outcome: major_revision

Abstract
The trihexagonal tiling system exhibits strong electron-electron interactions, positioning it as a key condensed matter platform for studying geometrically frustrated lattices made up of corner-sharing triangles. Its phase-transition-driven lattice modulations enable Fermi surface reconstruction, while emergent van Hove singularities near the Fermi level and correlated band anomalies present critical challenges in understanding electronic interaction mechanisms. By combining temperature-dependent spectroscopy, angle-resolved photoemission, and density functional theory calculations, we demonstrate a 61-fold enhancement in terahertz direct detection mode, ultra-low noise (1.38×10⁻²⁵ A²/Hz) below phase transition temperature, and broadband operation up to 100 GHz in beat-note heterodyne mode. These results are directly correlated with the Fermi surface reconstruction induced by phase transitions. This work positions geometrically frustrated lattices as a powerful platform for studying correlated quantum phenomena, offering new pathways for the design of advanced quantum devices.

Introduction
The geometrically frustrated lattice, a network of corner-sharing triangles, represents a foundational platform in condensed matter physics for hosting a spectrum of exotic quantum states. It normally causes Fermi surface reconstruction coupled with singularities in the electronic band structure at the Fermi level (E F). These diverse quantum states include: charge density wave (CDW), spin-liquid states, orbital magnetism, pair density wave (PDW), and unconventional superconductivity. Van Hove singularity (VHS) can drive diverse quantum phenomena; however, their implications for responses to different types of electromagnetic probes (e.g., light) remain underexplored. VHS near the E F can be achieved through graphene-based Moiré superlattices. Current fabrication strategies for advanced optoelectronic devices, which rely heavily on mechanical stacking and chemical vapor deposition (CVD) techniques, face significant limitations that hinder the development of robust and scalable applications. In contrast, VHS can naturally occur in kagome lattices, providing a compelling alternative platform. By harnessing VHS-dominated optoelectronic transitions, such platforms offer a viable pathway for next-generation quantum applications.

The discovered family of materials AV₃Sb₅ (A=K, Rb, Cs), which crystallizes in the hexagonal space group P6/mmm, provides an ideal platform for investigating correlated quantum phenomena. The novel physical properties of the AV₃Sb₅ family have been extensively investigated. Recent breakthroughs include mechanistic studies of superconductivity in CsV₃Sb₅, novel perspectives on symmetry breaking from KV₃Sb₅ research, and laser-STM demonstrations of strain-mediated symmetry control in RbV₃Sb₅ (RVS). The density of states (DOS) at 2D VHS exhibits logarithmic divergence at saddle points while remaining non-divergent at band extrema. This establishes the fundamental importance of VHS in kagome material research. Undoubtedly, the integration of low-energy photon detection techniques enables deeper exploration of VHS in the band structure near the E F of kagome materials. This approach offers unique insights into the distinctive electronic phenomena associated with kagome metals.

In this study, we systematically investigate the low-energy photon detection mechanism in kagome materials through a combined approach of variable-temperature measurements, band-structure observations, and first-principles calculations. By constructing symmetry-engineered electrode antennas on hexagonal lattices, we demonstrate a remarkable nonlinear enhancement in photoresponse under low-energy photon excitation at varying frequencies, mediated by VHS near the E F in RVS. Our custom-designed cryogenic temperature system enables direct observation of VHS-governed exotic phenomena through low-energy direct/beat-note heterodyne configurations. The device exhibits exceptional performance across microwave to terahertz (THz) frequencies, achieving: 61-fold photoresponse enhancement in direct detection mode, ultra-low noise (1.38×10⁻²⁵ A²/Hz) below phase transition temperature (T CDW), broadband operation up to 100 GHz in beat-note heterodyne mode. These results establish a direct correlation between VHS at the E F and light-matter interactions, and elucidate the intrinsic photodetection mechanisms in kagome materials. This work not only provides fundamental understanding of the pivotal role of VHS in governing the extraordinary optoelectronic properties of quantum kagome systems, but also underpins a technical landscape of a kagome material as a universal building block for sensing and energy-harvesting systems that become increasingly ubiquitous nowadays in the studied frequency range.

Results
VHS-driven photodetection mechanism
RVS system consists of planar V-atom kagome networks, intervening Sb honeycomb layers, and triangular Rb-ion planes separating the V-Sb slabs. RVS undergoes a CDW phase transition at T CDW (~102 K), which is accompanied by substantial electronic band structure reconstruction, building upon prior research on kagome systems. Figure 1b, c illustrate three key electronic band features of an ideal kagome lattice at the normal state: (i) Dirac cones at the K point, (ii) VHS at the M point, and (iii) momentum-space flat bands. Figure 1d, e illustrate the unit cell configurations of RVS in the normal state and CDW state, respectively. The CDW transition in RVS, within a simple planar case, yields a 2×2 long-range charge ordering pattern, causing an Inverse Star of David (ISD) structure in the plane characterized by a doubling of the primitive cell. Figure 1f presents the electronic band structure at the normal state computed along the Γ-K-M-Γ symmetry line, revealing the predicted pair of VHSs flanking E F near the M point (designated as VHS1 and VHS2 in Fig. 1f). The VHS1 and VHS2 near the E F exhibit complementary dispersion relations—electron-like along Γ-M and hole-like along M-K. This generates a divergent DOS, as confirmed by our calculations. Utilizing the divergent DOS at VHS, we demonstrate photoelectric conversion across both normal and CDW phases (Fig. 1g). Notably, upon entering the CDW state (T<T CDW), the VHS near the M point progressively shifts away from the E F (Fig. S7). This unique VHS redistribution provides a well-defined mechanism for photoresponse enhancement of non-equilibrium carrier transition probabilities (Fig. 1g), which is systematically analyzed in subsequent sections.

Singular electronic band behavior in RbV₃Sb₅
To elucidate the photoelectric detection mechanisms in RVS, we perform density functional theory (DFT) calculations and angle-resolved photoemission spectroscopy (ARPES) observations (Methods). Our comparative analysis between theoretical and experimental results elucidate the emergence of VHS3 in the CDW phase. The exceptional crystalline quality of the material (detailed in Supplementary Note 1) ensures experimental reproducibility. Figure 2a presents the temperature-dependent in-plane resistivity of RVS, revealing a distinct anomaly at approximately 102 K. This feature is characteristic of a CDW phase transition, consistent with established observations in correlated electron systems. As established in prior investigations, the T CDW exhibits pronounced thickness dependence in AV₃Sb₅ materials. Our systematic study employs an approximately 140 nm-thick sample—a dimensionality carefully selected to maintain bulk-like electronic properties while avoiding the 3D-to-2D crossover regime. Additionally, our results reveal that the pristine phase exhibits marked structural instability. Phonon spectrum, performed on a 3×3×1 supercell, reveals significant phonon mode softening around the M and L points of the Brillouin zone (BZ) boundary in the RVS phonon dispersion (Fig. 2b), unambiguously indicating inherent structural instability in the pristine phase. This lattice dynamical instability serves as the driving mechanism for the CDW phase transition.

By combining theoretical and experimental results, we focus our investigation on a unique feature in the electronic band structure: VHS. Figure 2c displays the DFT-derived electronic structure of RVS, showing orbital-projected (V 3d, Sb 5p) band dispersions in the primitive lattice with (colored) and without (gray) spin-orbit coupling (SOC). Three key characteristics are observed: (i) a dispersionless band across nearly the whole BZ at 1.00±0.05 eV above E F, (ii) Γ-centered electron pockets and Dirac cones dominated by V 3d states near the K point, and (iii) multiple VHSs near M (black arrows) arising from V 3d-Sb 5p hybridization. The VHS1 and VHS2 are particularly significant, positioned within 10 meV of E F and exhibiting complementary dispersion relations—electron-like along Γ-M and hole-like along M-K. This generates a divergent DOS, as confirmed by our calculations.

For low-energy photon detection, we systematically investigate the VHS near the E F in the normal phase and CDW phase. Calculated and ARPES-measured band structures along the high-symmetry paths demonstrate exceptional consistency (Fig. 2d, e). Despite thermal broadening effects at elevated temperatures, we identify two pivotal phenomena: (i) a well-defined hole-like band dispersion along the K-M high-symmetry path, and (ii) the dominant contribution of V d-orbital states to the formation of the VHS. VHS1 manifests hallmark VHS characteristics, exhibiting contrasting dispersion relations along the M–Γ (upward) and M–K (downward) directions. This characteristic leads to a pronounced DOS peak near E F. Figure 2f, g respectively show the theoretically predicted band structure of the ISD state and corresponding ARPES measurements (T<T CDW). The strongly dispersive band along the K-M undergoes a significant downward shift (~0.14 eV at the M point) relative to the normal state, thereby forming a distinct VHS1.

Intriguingly, near the midpoint of the M-K trajectory, the V d-orbital hybridization shows discontinuity and a CDW gap is open. Correspondingly, the part of the band below the E F also undergoes a downward shift, moving entirely below E F. This is clearly captured at ~0.09 eV below E F in the low-temperature experimental results. More intriguingly, a new VHS configuration emerges here, characterized by a hole-like pocket along the M-K direction and an electron-like pocket in the perpendicular direction. A detailed analysis of the band structure at T CDW (Fig. 2h, second-derivative plot along the Γ-K-M-Γ) reveals a new VHS3 (~0.09 eV below E F) near the M-K midpoint (pink marker).

To further verify the characteristics and momentum location of VHS3, Fig. 2i demonstrates exceptional consistency between cryogenic temperature DFT calculations and cryogenic temperature ARPES-derived Fermi surfaces, featuring spectral cuts (1-5) at discrete k x positions along the K-M-K path. A systematic examination through ARPES cuts (Fig. 2i, j) unambiguously establishes the saddle-point character of VHS3. The data show that the band maintains an electron-like dispersion along k y (yellow dashes) at all k x positions, while hole band features (green dashes) with varying k x, which confirms the saddle point. The temperature evolution of the electronic band structure along the K-M-Γ path is annotated in Fig. S7. The downward shift of the V d bands and the formation of new VHS lead to a high DOS crossing the E F, thus leading to electronic structure instability. The calculated DOS exhibits robust agreement with the experimental findings. In both the normal state and CDW state, the DOS exhibits a peak at the saddle point due to the accumulation of occupied states where the electronic band dispersion exhibits a vanishing group velocity (detailed in Supplementary Note 4). Additionally, while the in-plane orbital-dominated Dirac bands near K remain essentially unaffected, the Γ-point electron pocket—composed primarily of out-of-plane p z orbitals—exhibits a pronounced energy shift. This collective behavior provides definitive evidence for a temperature-driven phase transition with Fermi surface reconstruction. These findings demonstrate that VHSs emerge from band structure extrema and saddle points occur at strategic locations that fundamentally govern optoelectronic response.

VHS-governed exotic phenomena through direct configurations
Our analysis reveals that RVS undergoes significant topological modifications near its T CDW, manifesting as band structure evolution, Fermi surface reconstruction, and pronounced VHS rearrangements. These emergent properties create unprecedented opportunities for low-energy photon detection. Our work demonstrates—for the first time—the direct utilization of kagome-derived topological states for photodetection. We now present the remarkably promising experimental results in photodetection.

We develop the structure of the kagome-metal-based photodetector (Fig. 3a), comprising a bowtie antenna-which serves as electrodes and features a left-right symmetric optical field efficiently coupling photon energy into the channel-and the kagome material RVS. The RVS channel layer is prepared by mechanical exfoliation, and the device is meticulously patterned into a planar configuration. (further details are provided in the Methods). Complete finite-difference time-domain (FDTD) simulation details are provided in Supplementary Note 5.

The energy distribution curves (EDCs) extracted near the E F region (Fig. 3b) demonstrate the dynamic evolution of the RVS system’s band structure with decreasing temperature (from 130 to 10.5 K). In the normal state (T>T CDW), both VHS1 and VHS2 at the M-point maintain their positions and exhibit minimal temperature dependence. In the CDW state (T<T CDW), the electronic states near the M-point undergo a progressive shift toward higher binding energies with decreasing temperature (further details illustrated in Fig. S7). In kagome systems exhibiting Fermi surface nesting characteristics, these observations provide key insights into the microscopic physical mechanisms underlying electronic instabilities. The VHS exhibits intrinsic electronic instability. Fermi surface nesting facilitates enhanced electron scattering along its characteristic wavevector. Simultaneously, the emergence of a new VHS3 feature leads to a significant amplification of the DOS at the E F. The strongly enhanced DOS at these singularities creates ideal conditions for low-energy photon detection. Figure 3c elucidates the microscopic mechanism governing the enhanced photoresponse, showing that the VHS-induced DOS peak increases the number of available initial states for the optical transition.

Our full-spectrum analysis reveals distinct temperature-dependent photoresponse characteristics of the photodetector across three key THz bands (0.02–0.04, 0.08–0.1, and 0.33–0.355 THz) at 0 mV bias. Figure 3d–f demonstrate that the photoresponse intensity, color-graded from dark to light blue (strongest to weakest), consistently peaks at T CDW ~102 K in all frequency ranges. The top-view schematics (Fig. 3d–f, insets) spatially resolve these response maxima. As the photocurrent intensity exhibits a positive correlation with the DOS, we derive the quantitative relationship expressed in Eq. 1.

J(ω) ∝ e D(E) |⟨f| H^ int |i⟩|² ℏω Φ(ω) (1)

where J(ω) denotes photocurrent density, e represents electron charge, D(E) corresponds to the electronic DOS, ⟨f| H^ int |i⟩ describes transition matrix element incorporating initial state, final state, and perturbation Hamiltonian, ℏω is incident photon energy, Φ(ω) describes incident photon flux. As clearly demonstrated by the simplified Eq. 1, the photocurrent density is directly influenced by the electronic DOS. In the normal state of kagome metal RVS, two VHSs exist near the E F at the high-symmetry M-point. CDW phase transition renormalizes the band structure and new VHS emerges. Since the electronic DOS exhibits logarithmic divergence near VHS, the phase transition therefore enhances the photocurrent density J(ω) through increased D(E).

Under an applied bias of 100 mV, we systematically measured the temperature-dependent photoresponse of the RVS-based detector at 0.03, 0.09, and 0.35 THz (Fig. 3g). Experimental results indicate that at T CDW (~102 K), the device’s photoresponse exhibits significant nonlinear enhancement. Notably, applying a 100 mV bias maintains the peak frequency while significantly enhancing the photocurrent intensity (full spectral scans available in Supplementary Note 8). This enhancement mechanism arises from bias-excited electronic transitions between VHS.

Figure 3h compares the photoresponse enhancement between the normal and CDW phases at a 100 mV bias, revealing frequency-dependent amplification factors of 60.82 × (0.03 THz); 12.64 × (0.1 THz); and 3.18 × (0.35 THz). This enhancement aligns with the theoretical predictions: the phase transition redistributes VHS and modifies the electronic DOS near critical points, thereby amplifying interband transitions. Our results establish kagome materials as a platform for frequency-selective photoresponses through many-body correlations.

The second-order photocurrent (I ph) scaled linearly with the incident electric field power (P in) across temperatures (77–300 K), as shown in Fig. 3i. The photodetector exhibits ideal linearity over more than two orders of magnitude in P in and the data are well fitted with a simple power law (I ph ∝ P in^α, α=0.99±0.005) at all measured temperatures. This temperature-independent nonlinearity is a direct manifestation of the RVS system’s singularelectronic structure, where VHS-derived DOS enhances multiphoton processes. Our results establish kagome materials as a unique platform for wide-temperature-range nonlinear photonics.

Noise is a critical parameter influencing the performance of optoelectronic devices. Once the temperature is below T CDW, the electronic noise spectral density shows a dramatic reduction by over two orders of magnitude (from 3.8×10⁻²³ A²/Hz² to 1.38×10⁻²⁵ A²/Hz²). The system exhibits enhanced stability upon entering the CDW state, with significantly reduced random carrier scattering events. The Noise Equivalent Power (NEP) is a critical parameter. Across the entire modulation frequency range, the device achieves an average NEP of approximately 20 pW/Hz¹/². Operating at 0.1 THz, our device demonstrates ultrafast response characteristics with 580 ns rise time and 520 ns fall time, which is several orders of magnitude faster than other thermoelectric detectors (such as ≈ 170 µs of tellurium nanowire photodetector). (see details in Fig. S12)

VHS-driven heterodyne mixing from millimeter wave to THz band
Based on the unique VHS properties as well as band-renormalization of kagome-metals, we further investigate the potential of heterodyne detection. In our measurements (details can be found in Methods), the fabricated kagome material-based mixer serves as a frequency conversion device in the circuit (Fig. 4a), which constitutes a critical component in modern RF communication systems.

The heterodyne THz detection system, governed by novel physical mechanisms, achieves broadband operation and high detection sensitivity across phase transitions. The schematic illustration of the mixing process under optical beating with in two different frequencies in kagome-based materials is presented in Fig. 4b. The kagome material-based mixer generates distinctive heterodyne signals through coupling of the local oscillator (f LO) and radio frequency (f RF) inputs, yielding an intermediate-frequency beat signal V IF described by:

V IF(t) = L 0(t) R THz(t) = L o R THz/2 * cos(ω LO - ω THz)t + cos(ω LO + ω THz)t (2)

where V IF(t) represents the intermediate frequency output signal, L 0(t) represents the local oscillator signal, R THz(t) represents the radio frequency signal. First, we demonstrate harmonic mixing in a kagome material-based mixer under collimated 6.5 GHz excitation. Through spectrum analysis, the first, second, and third harmonic comb lines are clearly resolved, with the harmonic signals exhibiting robust power dependence. Notably, the generated frequency comb also serves as a tunable local oscillator (f LO), enabling versatile heterodyne mixing. The measured f IF adheres precisely to the expected relationship: f IF = f RF – n f LO (n∈ℕ+) (Figure S14).

Through temperature-dependent measurements, we implement heterodyne mixing techniques in kagome-material-based mixers to systematically investigate their potential for modern communication technologies. Figure 4c demonstrates the temperature evolution of f IF signal arising from the distinctive VHS inherent to kagome systems. To ensure reliable characterization of mixing dynamics within the spectrum analyzer’s bandwidth constraints, we implement a heterodyne scheme using 22.4 GHz (f LO) and 23.4 GHz (f RF) signals. Control experiments with three independent mixers confirmed the reproducibility of our observations. Notably, we observe a pronounced enhancement in f IF signal intensity as the temperature decreased from 300 K to below T CDW. This anomalous behavior originates from temperature-induced modifications in the electronic band structure: (i) the emergence and upward energy shift of a VHS at the M-point, and (ii) the formation of a secondary VHS at the R-point below T CDW. The cooperative migration of these singularities enhances electronic transitions, resulting in the observed macroscopic amplification of the f IF signal.

Kagome systems exhibit exceptional promise for self-mixing applications as noted above. Building on this foundation, we observe broadband multi-wave-mixing in nonlinear kagome systems. Figure 4d demonstrates the characteristic signatures of subharmonic N-wave mixing (WM) (f LO is 23.4 GHz, f RF is 25.4 GHz and f IF signal is precisely captured by the spectrum analyzer). These peaks include three types of spectra: the two fundamental signals (ω₁=2πf LO, ω₂=2πf RF), the f IF signal (f IF = f RF - f LO), their higher-order modes, and the WM components (n f LO ± m f RF, where n, m=1, 2, 3…). The highest observed components reach up to 5 (f RF - f LO) and 6 f LO - 5f RF. These results indicate that, due to the material’s highly complex Fermi surface and exotic electronic behavior below T CDW, a frequency comb-like heterodyne mixing effect can be generated, with higher-order components extending up to the fifth order.

To further investigate the dynamic range of the kagome material-based mixer, the relationship between the f IF signals of different harmonic mixing orders and the incident power (P LO and P RF) is shown in Fig. 4e. The relationship follows the power law, P out = α P in (where P in = P RF), and the solid line represents the slope of the output power measured in the experiment. Notably, even when the f IF signal is set to its lower limit (P RF = -25 dBm, P LO = 14.8 dBm), the f IF signals at (f RF - f LO) and (2f LO - f RF) remain clearly detectable. This indicates that the minimum power excitation threshold of the mixer can be less than -25 dBm, demonstrating the potential of kagome materials for precise carrier frequency information acquisition.

By harnessing the exotic electronic properties of kagome material, we demonstrate the mixing range to the THz band for modern RF communication systems. The f LO is increased to above 100 GHz, approaching the electrical oscillation limit of micron-scale devices. Simultaneously, the f RF is tuned across a range from the Ku and Ka bands to the W band, as shown in Fig. 4f. This shows that the kagome-based device demonstrates intrinsic frequency-agile capture capability, operating across a very wide bandwidth of 1–100 GHz. The conversion loss (CL) increases from 20.1 ± 0.2 dB to 57.5 ± 0.2 dB at 100 GHz. This performance highlights the device’s promising applicability in next-generation wireless communication systems.

The frequency CL, defined as one of the key metrics for mixers, is expressed as:

CL = P in / P out = 10 log (30 P RF / P IF) (3)

where, 30 represents the gain coefficient of the LNA, S λ=λ²/4π represents the diffraction-limited area within the incident wavelength; S represents the area of the waveguide flare. The CL of the mixer near 100 GHz is 57.5 ± 2 dB, while the CL in the RF band is 20 ± 2 dB.

Methods
Crystal growth and characterization
Single crystals of RbV₃Sb₅ were grown via flux-based growth technique. The precursor RbSb was prepared by reacting Rb (purity 99.75%) and Sb granules (purity 99.99%) at 300 °C. Starting materials of RbSb, Sb and V powder (purity 99.99%) were loaded inside a Canfield crucible with a molar ratio of 3:9:1, sealed in a quartz tube. The assembly was heated up to 1100 °C in a furnace within 12 h and kept at this temperature for 10 h. It was subsequently slowly cooled down to 800 °C at a temperature decreasing rate of 50 °C/h and kept for 5 h, and then slowly cooled down further to 450 °C at 2 °C/h. Finally, the assembly was taken out from the furnace and decanted with a centrifuge to separate RbV₃Sb₅ single crystal from the flux. With the exception of sealing and heat treatment procedures, all other preparation processes were conducted in an argon-filled glove box to prevent reaction of Rb with atmospheric oxygen and moisture.

Atomically resolved the scanning transmission electron microscope measurement
The atomic arrangement was examined using a double aberration-corrected Thermo Scientific Spectra 300 STEM (Thermo Scientific, USA), operating at 300 kV with a convergence angle of 25 mrad and a collection angle ranging from 70 to 250 mrad. HAADF STEM images were acquired with a dwell time of 10 s per pixel.

Angle-resolved photoemission spectroscopy measurement
ARPES was used to characterize kagome metal RbV₃Sb₅ samples. The ARPES measurements were conducted at the BL-03U beamline of the Shanghai Synchrotron Radiation Facility, using a Scienta Omicron DA30 analyzer. The photon energy is 86 eV. The energy and angular resolutions were set to better than 50 meV and 0.02 Å⁻¹, respectively. Samples were cleaved in situ under ultrahigh vacuum conditions, revealing flat and mirror-like (100) surfaces. During measurements, the temperature was maintained at T~9 K, and the pressure in the main chamber was kept below 7×10⁻¹¹ torr.

First-principles calculations and theoretical modeling
We performed first-principles calculations using the Vienna ab initio simulation package with the projector augmented-wave method. The exchange-correlation energy was treated with the generalized-gradient approximation functional of Perdew-Burke-Ernzerhof. The plane-wave basis was employed with a kinetic-energy cutoff of 600 eV, and the k-space integration was performed with 9×9×4 and 4×4×4 k-meshes for the pristine cell and 2×2×1 supercell, respectively. All atoms were allowed to relax along the calculated forces until all the residual force components were less than 0.001 eV/Å. The calculated lattice parameters of the pristine structure are a=b=5.472 and c=9.073 Å. The spectral function A(k, E F) on the Fermi Surface was computed using WANNIER90 and WANNIERTOOLS, where the maximally localized Wannier functions were constructed by projecting the Bloch states onto V-d and Sb-p atomic orbitals. The phonon spectrum for the pristine phase was calculated using the finite displacement method with 3×3×4 k-points and a 3×3×1 supercell.

Device fabrication
Under room temperature conditions, optoelectronic devices were fabricated through mechanical exfoliation. The high-quality RbV₃Sb₅ sample was mechanically exfoliated onto blue tape (Shanghai Onway Technology Co., Ltd) and then directly transferred onto a high-resistivity silicon (ρ=20,000 Ω·cm) substrate coated with a thin SiO₂ oxide layer (300 nm), resulting in an RbV₃Sb₅ thin film. The antenna structure was patterned, and the contact area was defined using electron beam lithography, followed by etching. Cr/Au was deposited onto the material via electron beam evaporation to establish the electrical contact. The optoelectronic detector was fabricated following the metal lift-off process.

Performance measurement
The electrical characteristics of the detector at room temperature were obtained using a Keithley 4200A-SCS Parametric Analyzer. For optical measurements, the THz frequency was tuned to 0.30 THz (WR 2.8 tripler) and 0.12 THz (WR 9 tripler) using a VDI multiplier connected to a 40 GHz microwave source (Agilent E8257D). The optical response was modulated with a TTL signal at a frequency of 1 kHz and recorded using an oscilloscope, after passing through a low-noise voltage preamplifier (SR570) and a lock-in amplifier (SR830). The power density of the THz radiation was measured using a commercially calibrated photomixing THz power meter (TK100), with measurements taken at 2.5, 1, and 1 mW cm⁻² for frequencies of 0.04, 0.12, and 0.30 THz, respectively.

Heterodyne-mixing characterizations
A heterodyne is a signal frequency that is created by combining or mixing two other frequencies using a signal processing technique called heterodyning, which was invented by Canadian inventor-engineer Reginald Fessenden. Heterodyne mixing can be understood by analogy to musical beats-when two slightly different musical notes are played simultaneously, we hear a pulsating ‘beat’ at the difference frequency between them. Similarly, in heterodyne mixing, two signals at different frequencies (local oscillator and radio frequency) are combined in a nonlinear device (the mixer), producing new signals at the sum (f RF + f LO) and difference (|f RF - f LO|) frequencies. In our measurements, the fabricated mixer (kagome material-based detector) serves as a frequency conversion device within the circuit (Fig. 4a), constituting a critical component in modern RF communication systems. The differential frequency (referred to as the intermediate frequency) is selectively utilized because it enables easier electronic processing compared to the original high-frequency signal.

The mixing system at cryogenic temperature primarily consists of two major modules: the heterodyne mixing optical path and the cryogenic temperature refrigeration system. As shown in the lower-left part of the Fig. 4a, the system includes essential components for modern wireless communication—the f LO signal and the heterodyne f RF signal. The f LO signal is collimated using a TPX (polymethylpentene) lens with a focal length of 100 mm and directed onto a beam splitter. The f RF signal is incident on the beam splitter via an off-axis parabolic mirror (OAP), which focuses the millimeter-wave/THz beam. The optical signal is then precisely combined and directed onto the mixer after passing through the Dewar window (Sapphire). Different frequency bands requires specific THz sources. For microwave mixing in the 0–67 GHz range, a microwave source (Agilent E8257D, 0.02–0.04 THz) and a vector network analyzer (Ceyear) are used to provide the f LO and f RF signals, respectively. For the mixing configuration in the 0.08–0.12 THz range, the Agilent E8257D microwave source (0.02–0.04 THz) is connected to a VDI multiplier (WR 9.0) and a 100 GHz source (TeraSense). The f IF is fed into a LNA (ultra wide band=0.01–20 GHz, gain=30 dB Typ, noise figure=2.5 dB). The amplified f IF signal was then measured using a spectrum analyzer (0–27 GHz). Meanwhile, the other path of the optical signal passing through the beam splitter is accurately directed onto a TK power meter to calibrate the optical power. The right half of the figure depicts the low-temperature refrigeration module, which comprises a 77 K Closed Cycle Cryogenic System manufactured by Shanghai Lind Precision Instruments Limited.

In the higher-order harmonic mixing section, the f LO signal is used to generate higher-order harmonics signals (n f LO, where n ranges from 1 to 6) at the point of incidence. These generated signals are then mixed with another RF signal to produce an IF signal, denoted as (n f LO - f RF).

Data availability
Relevant data generated in this study are provided in the article and Supplementary Information. All raw data that support the plots within this paper and other findings of this study are available from the corresponding authors upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors have successfully developed a low-energy photon detector based on a Kagome material. Using ARPES on RVS, they observe an electronic phase transition below TCDW​ that brings van Hove singularities (VHS) close to the Fermi level. They demonstrate the critical role of VHS in driving electronic instability and related exotic phenomena, reporting a substantial enhancement in photoresponse by a factor of 62. However, several points require clarification, particularly regarding the ARPES and DFT results and the link between VHS and the enhanced photoresponse, before the manuscript can be considered for publication:\n1) As the authors note in the introduction, VHS are expected to show a logarithmically divergent DOS, similar to what was observed in twisted bilayer graphene by D. Marchenko et al. (Sci. Adv. 4, eaau0059 (2018)).\na) The manuscript claims that DFT calculations confirm a divergent DOS, yet no such figure is presented in the main text. Possibly this refers to Supplementary Figure S6?\nb) Even in that supplementary figure, there does not appear to be a logarithmic divergence where the VHS is expected. Rather, the peak shown resembles a standard DOS maximum typical of any band edge. The same observation holds for the experimental EDCs. Could the authors clarify?\nc) Are the EDCs integrated over the full momentum space? If so, it might be more informative to integrate only over regions near the VHS bands, to minimize contributions from other bands at similar energies.\nd) Regarding the DFT DOS, is the integration performed over the entire Brillouin zone? It would be helpful to see how the DOS behaves specifically along the Γ-M-K directions.\ne) Including these figures in the main text rather than in the supplementary materials would improve the clarity and impact of the discussion.\n2) It would be beneficial if the authors could provide constant energy contour (CEC) plots at the Fermi level, both below and above TCDW​, to more clearly illustrate the reported Fermi surface reconstruction.\n3) Colorbars are missing in most panels of Figure 2.\n4) At line 155, the authors state that a distinct hole-like band along K–M flattens at binding energies below 0.3 eV. This feature is not readily apparent in the figures. Could they specify where this band is located?\n5) The downward shift of the VHS3 band with decreasing temperature is noted, and the authors suggest this leads to a high DOS at the Fermi level, causing electronic instability. Further elaboration on the physical mechanism behind this instability would be appreciated.\n6) Based on the data, it appears that VHS1 and VHS2 shift downward upon the phase transition, and there is a subsequent change in the dispersion of VHS2, which the authors later refer to as VHS3. Is this interpretation accurate?\n7) In Figure 2e, VHS1 (and possibly VHS2) remains at the Fermi level even above TCDW​ along the M–K direction. Given EDC (ARPES) and DOS (DFT) intensity near the Fermi level does not change dramatically, should we not also expect significant photoresponse above the transition? How do the authors confirm that the observed enhancement is directly linked to the presence of VHS?\n8) The manuscript reports the strongest photoresponse enhancement at 0.03 THz. Could the authors provide an intuitive explanation for this frequency dependence? A simple depiction of the underlying mechanism and the nature of the optical transition would help.\n9) For readers not familiar with heterodyne mixing techniques, a simplified explanation of the measurements shown in Figure 4 would be helpful.", "reviewer_2": "The authors explained the optoelectronic response of RVS in terms of charge density waves and VHS. All experimental data look clear, but there are many unclear descriptions in the manuscript. Even though the manuscript shows good data on optoelectronic properties related to the CDW gap, I am sorry that I cannot recommend the current manuscript for publication in Nature Communications.\nMajor comment\n1. I cannot understand why the authors are emphasizing Moiré superlattices in the manuscript.\nThe experiments are not directly connected with Moire physics; the work is a pure story of charge density waves(CDW) and Fermi surface nesting. Please explain the clear reason why the authors can connect the current work with Moiré physics.\n2. I can agree on the explanation for VHS1 and VHS2. But VHS3 is not. In the case of VHS1 and VHS2, the author's claim is valid because the points are located at the M point (Brillouin zone boundary). However, VHS3 is hard to claim as the saddle point, even though it is valid to explain as the singularity point for the density of states. It looks good to explain by the formation of CDW gap.\n3. The authors emphasized \"62-fold\" in the abstract and introduction, but there is no explanation.\nMinor comment\n1. (line 110) Electron pockets at Gamma are not shown in Figure 1 (b), but are shown in (f). So I think it is not proper.\n2. (line 85) What is the meaning and role of \"symmetry-engineered electrodes\"?", "reviewer_3": "The authors explore the possibility of utilizing the Fermi surface reconstruction associated with charge-density wave transitions in 2D van-der-Waals materials - specifically in the V-based kagome metal RbV3Sb5 - for photo-sensoric devices. Via ARPES and DFT calculations, they recall and highlight the temperature-dependent changes in the electronic band structure, with an emphasis on a van-Hove singularity close to the Fermi level. Exploiting these Fermi-surface features, they demonstrate a photocurrent detection capabilities of a RbV3Sb5-based detector device.\nWhile this work tackles an underexplored aspect of kagome metals which may open the door to future applications, there are several issues that deserve attention, clarification, and improvement before considering the manuscript for publication.\n- The authors assume an inverse-Star-of-David as the CDW pattern in RbV3Sb5. As far as I understand, the precise pattern is still an open issue (although recent works seem to slightly favor an inverse-Star-of-David over a star-of-David pattern). Can the authors elaborate on their assumption? I suggest they also plot the electronic band structure for a star-of-David pattern for comparison and comment on the fundamental differences between those two (if any).\n- Related to the former comment is the issue of potential stacking faults, which are known to occur in V-based kagome materials depending on the cleavage procedure as well as the cooling rate. The authors should discuss these potential effects, as they may be highly relevant for future fabrication and application processes.\n- In Fig. 2a, the resistivity curves from three different samples show transition temperatures between 92 K and 102 K. Meanwhile, the authors emphasize an \"outstanding single-crystal quality\". Please discuss in the manuscript the potential origin of the wide range of transition temperatures.\n- The authors also speculate about softening of acoustic modes \"possibly evidencing a structural instability\" - there have been numerous studies detailing el-el and el-ph coupling, and the role of crystal structure on the CDW formation AV3Sb5, so I don't get why the authors need to describe it in these vague terms. Better to add some relevant references at this point.\n- I find some of the phrasing related to the ARPES results somewhat confusing. I get that the authors want to present their ARPES results to link features of the electronic band structure to photo-sensoric activity of RbV3Sb5. However, in my view the electronic (CDW) phase transition has been heavily studied and well-established for years. Yet, parts of the text read as if nothing is known so far about the electronic structure. Take for example: \"Compelling evidence of electronic phase transitions in Kagome materials\". Am I missing some newly uncovered observation made by the authors for the first time? Otherwise, these ARPES results do not report any novel discovery or observation, hence there is no need to present them as \"compelling evidence\".\n- Finally, I would like to see a comparison of the photo-sensoric performance of RbV3Sb5 with other related vdW materials, as well as with other, conventional materials in the discussion, so that the readers may better appreciate the performance. Likewise, can the authors comment on potentially utilizing other CDW materials with a transition temperature closer to room temperature? Are there any fundamental advantages of V-based kagome metals?\nMinor issues:\n- Abstract: \"enhancement in in terahertz\"\n- Line 45: Add a reference at the end of the first sentence.\n- Line 47: Ref. 1 does not seem to be a proper, primary reference here.\n- Line 106: specify the value of T_CDW, add a reference at the end of the sentence.\n- \"Notably, upon entering the CDW phase (T < TCDW), the VHS near the M point progressively shifts away from the EF, while a new VHS forms at the R point.\": mark and illustrate these changes in Fig. 1 as well.\n- Lines 241-243 and lines 249-250 are nearly identical.\n- Since Fig. 3b only contains 5 curves, it might be advantageous to simply plot all curves on top of each other to better appreciate the changes through the transition temperature."}, "author_response": "———— R E P L Y T O R E V I E W E R 1 ————\nReviewer #1 (Remarks to the Author):\n“The authors have successfully developed a low-energy photon detector based on\na Kagome material. Using ARPES on RVS, they observe an electronic phase transition\nbelow TCDW that brings van Hove singularities (VHS) close to the Fermi level. They\ndemonstrate the critical role of VHS in driving electronic instability and related exotic\nphenomena, reporting a substantial enhancement in photoresponse by a factor of 62.\nHowever, several points require clarification, particularly regarding the ARPES and\nDFT results and the link between VHS and the enhanced photoresponse, before the\nmanuscript can be considered for publication.”\nResponse:\nWe sincerely appreciate the reviewer’s positive comments and valuable\nsuggestions for improving the quality of our manuscript. Each of your constructive\npoints has been carefully addressed, and we have made the corresponding revisions and\nrewrites. We hope that the revised manuscript meets your expectations. We would like\nto once again thank the reviewers for their thorough and constructive feedback, which\nhas helped us improve the manuscript substantially.\nComment 1):\n“As the authors note in the introduction, VHS are expected to show a\nlogarithmically divergent DOS, similar to what was observed in twisted bilayer\ngraphene by D. Marchenko et al. (Sci. Adv. 4, eaau0059 (2018)).\na) The manuscript claims that DFT calculations confirm a divergent DOS, yet no such\nfigure is presented in the main text. Possibly this refers to Supplementary Figure S6?\nResponse:\nWe sincerely appreciate the Referee’s insightful questions. Figure S6 illustrates\nthe divergent DOS obtained from density functional theory (DFT) computations.\nFollowing the reviewer's suggestions, we have updated Figure S6 (Fig. R1) with\nrecalculated results. We also add a discussion of the DOS calculation results in the main\ntext. We presented the specific details in the response below.\nb) Even in that supplementary figure, there does not appear to be a logarithmic\ndivergence where the VHS is expected. Rather, the peak shown resembles a standard\nDOS maximum typical of any band edge. The same observation holds for the\nexperimental EDCs. Could the authors clarify?\nResponse:\nWe sincerely appreciate the reviewer's insightful observation regarding the VHS\n1 / 32\ncharacteristics in our data. Below we provide a detailed response addressing the specific\nconcerns about the EDCs and the DOS peak shape.\nIn theoretical discussions, DOS calculations were performed by integrating across\nthe entire Brillouin zone including contributions from the z direction, with results\npresented in Fig. S6. Based on your suggestion, we computed the DOS along the high-\nsymmetry directions Γ–M–K. These refinements significantly improved the precision\nof our DOS results. In the updated calculations (Fig. R1 b), we observed a pronounced\nDOS peak corresponding to the VHS.\nInitially in the EDCs, we presented data collected along the entire Γ-M-K line,\nensuring the inclusion of sufficiently rich band features. Since a VHS does not occupy\na large momentum space like a flat band, its peak feature in the EDCs will be weakened.\nBased on your suggestion, we have performed additional data analysis over regions\nnear the VHS bands. The arrows on this curve indicate the contribution of VHS3. This\ncurve clearly demonstrates the process in which the VHS position moves deeper below\nthe Fermi level (E ) with decreasing temperature.\nF\nIn response to the reviewer's suggestions, we have revised the DOS calculations\nand EDC analysis, with the updated results now incorporated into Figure R1 (Fig. S6).\nRevised Figure R1 (Supplementary Figure S6) a Temperature-evolved EDCs at VHS3 of\nRbV₃Sb₅. b Comparative density of states (DOS) spectra showing the electronic structure of RVS\nin its normal state (purple) and CDW phase (light blue).\nc) Are the EDCs integrated over the full momentum space? If so, it might be more\ninformative to integrate only over regions near the VHS bands, to minimize\ncontributions from other bands at similar energies.\nResponse:\nWe appreciate the Referee’s constructive suggestion. As previously mentioned, the\n2 / 32\nEDCs presented in Fig. S6a are derived from the entire Γ-M-K line. Based on your\nsuggestion, we have performed additional data analysis over regions near the VHS\nbands. We include additional EDC curves at the VHS3 point in Fig. R2 (Extended Data\nFig. 2), where a newly appearing peak at low temperatures effectively reflects the\nemergence of the new VHS.\nWe revised Figure S6 according to the reviewer’s suggestion.\nRevised Figure R1 (Supplementary Figure S6) a Temperature-evolved EDCs at VHS3 of\nRbV₃Sb₅.\nRevised Figure R2 (Extended Data Fig. 2) The temperature-dependent electronic band structure\nevolution along the K-M-Γ path. The orange trace marks the energy position of VHS3, as derived\nfrom the EDC analysis.\nd) Regarding the DFT DOS, is the integration performed over the entire Brillouin zone?\n3 / 32\nIt would be helpful to see how the DOS behaves specifically along the Γ-M-K\ndirections.\nResponse:\nWe appreciate the reviewer’s helpful suggestion regarding the visibility of the\nVHS peak in the DOS from Fig. S6 b. Based on the reviewer’s suggestion, we computed\nthe DOS along the high-symmetry directions Γ–M–K. We have carefully optimized k-\npoint grids and increased the NEDOS parameter (number of grid points within certain\nenergy range) in our calculations. In Fig. R1b (Fig. S6 b), we present the DOS data for\nboth the CDW state and the Normal state.\nWe have updated the theoretical calculations, and the revised results are presented\nbelow (Fig. R1 b):\nRevised Figure R1 (Supplementary Figure S6) Comparative density of states (DOS) spectra\nshowing the electronic structure of RVS in its normal state (purple) and CDW phase (light blue).\ne) Including these figures in the main text rather than in the supplementary materials\nwould improve the clarity and impact of the discussion.”\nResponse:\nWe thank the Referee for raising this important point. Following the reviewer's\nsuggestions, we have revised the DOS calculations and EDC analysis, with the updated\nresults now incorporated into Fig. R1(Fig. S6) and Fig. R2 (Extended Data Fig. 2).\nWe concerned that including these figures in the main text might potentially\ndistract the reader from the primary flow of the discussion and our key conclusions. In\nresponse, we have integrated a discussion of the DOS calculation results in the main\ntext. This ensures comprehensive coverage of the supporting evidence while preserving\nthe logical coherence and readability of the central discourse.\nThe corresponding discussions have been added in the revised manuscript:\n4 / 32\n“The calculated DOS exhibits robust agreement with the experimental findings. In both\nthe normal phase and CDW phase, the DOS exhibits a peak at the saddle point due to\nthe accumulation of occupied states where the electronic band dispersion exhibits a\nvanishing group velocity. DOS.” (Page 6, Lines 178-181)\nComment 2):\n“It would be beneficial if the authors could provide constant energy contour (CEC)\nplots at the Fermi level, both below and above TCDW, to more clearly illustrate the\nreported Fermi surface reconstruction.”\nResponse:\nWe sincerely thank the reviewer for the insightful suggestion. Based on your\nsuggestion, we provide constant energy contour plots for both below and above T\nCDW\nat the E . As shown in Figure R3a and b (Extended Data Fig. 1), we can see that the\nF\nISD Fermi surface exhibits a discontinuity along the M-K direction, which has also\nbeen highlighted in the red box, suggesting the presence of a band gap. Compared with\npristine case, the ISD pattern of CDW undergoes a Fermi surface reconstruction.\nThe theoretical calculation results are provided as follows:\nRevised Figure R3 (Revised Extended Data Fig. 1) The Normal-phase (a) and CDW-phase (b)\nFS sheets are displayed at 𝑘 =0, where the spectral function A (k, E ) is drawn using the color\n𝑧 F\nscale.\nComment 3):\n“Colorbars are missing in most panels of Figure 2.”\nResponse:\nWe sincerely thank the Referee for this thoughtful comment. To enhance data\ninterpretability, we have added color bars to Figure 2.\n5 / 32\nComment 4):\n“At line 155, the authors state that a distinct hole-like band along K–M flattens at\nbinding energies below 0.3 eV. This feature is not readily apparent in the figures. Could\nthey specify where this band is located?”\nResponse:\nWe thank the reviewer for bringing this point to our attention. We apologize for\nany confusion caused by our previous explanation. We have revised the original\ndescription of the band structure results in our manuscript.\n“Despite thermal broadening effects at elevated temperatures, we identify two pivotal\nphenomena: (i) a well-defined hole-like band dispersion along the K-M high-symmetry\npath; (ii) the dominant contribution of V d-orbital states to the formation of the VHS.\nVHS1 manifests hallmark VHS characteristics, exhibiting contrasting dispersion\nrelations along the M–Γ (upward) and M–K (downward) directions—which generates\na pronounced DOS peak near E .” (Page 5, Lines 149-155)\nF\nComment 5):\n“The downward shift of the VHS3 band with decreasing temperature is noted, and\nthe authors suggest this leads to a high DOS at the Fermi level, causing electronic\ninstability. Further elaboration on the physical mechanism behind this instability would\nbe appreciated.”\nResponse:\nWe sincerely thank the Referee for this thoughtful suggestion on the physical\nmechanism. RVS materials exhibit Fermi surface nesting, a characteristic wherein the\nFermi surface comprises extended parallel segments connected by a single wave vector\nin momentum space. This nesting feature, mediated by electron-phonon coupling, can\ndrive periodic lattice distortions, ultimately inducing a CDW phase transition. The VHS\nexhibits intrinsic electronic instability. Fermi surface nesting promotes enhanced\nelectron scattering along its characteristic wavevector. Simultaneously, the emergence\nof a new VHS3 feature, establishing an unstable electronic regime, leads to a significant\namplification of the DOS at the Fermi level. These synergistic effects collectively drive\npronounced electronic instabilities across the Fermi surface of the complex kagome\nsystem.\nThe corresponding physical mechanism explanations have been added in the\nrevised manuscript.\n“In kagome systems exhibiting Fermi surface nesting characteristics, the observation\nenhances our understanding of the microscopic physical mechanisms underlying\nelectronic instabilities. The VHS exhibits intrinsic electronic instability. Fermi surface\n6 / 32\nnesting promotes enhanced electron scattering along its characteristic wavevector.\nSimultaneously, the emergence of a new VHS3 feature leads to a significant\namplification of the DOS at the Fermi level33. The strongly enhanced density of DOS\nat these singularities creates ideal conditions for low-energy photon detection.” (Page 7,\nLines 210-215)\nComment 6):\n“Based on the data, it appears that VHS1 and VHS2 shift downward upon the\nphase transition, and there is a subsequent change in the dispersion of VHS2, which\nthe authors later refer to as VHS3. Is this interpretation accurate?”\nResponse:\nWe sincerely thank the Referee for this thoughtful comment. In RVS materials,\nprogressive cooling drives a CDW transition from the metastable normal phase.\nSystems displaying Fermi surface nesting, characterized by extended parallel segments\nof the Fermi surface connected by a single wave vector in momentum space, develop\nperiodic lattice distortions through electron-phonon coupling, inducing electronic state\nsplitting and consequent gap formation at the Fermi level. Notably, in kagome systems,\nthis mechanism simultaneously (i) displaces the VHS2 to lower binding energies and\n(ii) generates a CDW gap that cleaves the original feature into a resolved VHS3. While\nARPES is inherently limited to occupied states below the E , the synergistic\nF\ncombination of our experimental data with first-principles DFT calculations (Figs.\nR4a,b) provides definitive evidence for CDW mediated gap formation and the\nconsequent splitting of electronic states into a resolved VHS3. Specifically, in Fig. R4c,\nthe yellow-marked VHS3 does not extend into the Γ-M region, which is consistent with\nthe calculated results in Figs. R4a,b. However, through careful identification, we\ndemonstrate the existence of saddle points in Fig. R4d and Fig. R4f—a hole pocket\nalong the M direction and an electron pocket along the R direction—which aligns with\nrelated works (PhysRevLett.127.236401). The presence of VHS3 remains fundamental\nto the subsequent discussion.\nOur comprehensive data analysis confirms the emergence of a VHS3 after CDW\nphase transition.\n7 / 32\nRevised Figure R4 a,b Calculated DFT band structures of the CDW phase along high-symmetry\ndirections in the Brillouin zone are shown for two cases: (Fig. S5) (a) without SOC and (b) with\nSOC. c (Fig. 2h) Second derivative spectrum along the high-symmetry path M-K-Γ at 10.5 K (below\nT ). The dotted line enhances the visibility of the energy bands near the M point, clearly revealing\nCDW\nthe band structure around VHS1 and VHS3. d (Fig. S4b) Calculated CDW state and corresponding\nARPES intensity plot along the M-VHS3-R direction, with yellow dashed lines serving as guides\nto the eye. e (Fig. 2i) Experimental and theoretical Fermi surface comparison. Orange markers\nindicating the R direction. f (Fig. 2j) ARPES spectra from the momentum-space trajectories (cuts\n1-5) in Fig. 2i as indicated by grey lines. The yellow dashed line highlights the electron-like band,\nwhile the green dashed line indicates the hole-like band. The arrows in cut 3 indicate the appearance\n8 / 32\nof VHS3.\nComment 7):\n“In Figure 2e, VHS1 (and possibly VHS2) remains at the Fermi level even above\nTCDW along the M–K direction. Given EDC (ARPES) and DOS (DFT) intensity near\nthe Fermi level does not change dramatically, should we not also expect significant\nphotoresponse above the transition? How do the authors confirm that the observed\nenhancement is directly linked to the presence of VHS?”\nResponse:\nWe thank the reviewers for their insightful comments and propose that the\nanomalous photoresponse enhancement arises from the dynamic evolution of the VHS\nduring the phase transition. First-principles calculations of the DOS indicate a\npronounced DOS peak near the E post-transition (Fig. R1). ARPES further reveals\nF\nthat VHS1 at the high-symmetry M point shifts to higher energies, crossing the E upon\nF\ncooling. Simultaneously, electron-phonon coupling induces a CDW gap, prompting\nVHS3 to migrate toward higher energies below the transition temperature. These\nsynergistic effects generate a high carrier density near the E at the critical temperature,\nF\nultimately driving the macroscopic photoresponse enhancement. Our findings thus\nestablish a direct link between the observed phenomenon and VHS dynamics.\nRevised Figure R1 (Supplementary Figure S6) a Temperature-evolved EDCs at VHS3 of\nRbV₃Sb₅. b Comparative density of states (DOS) spectra showing the electronic structure of RVS\nin its normal state (purple) and CDW phase (light blue).\nComment 8):\n“The manuscript reports the strongest photoresponse enhancement at 0.03 THz.\nCould the authors provide an intuitive explanation for this frequency dependence? A\n9 / 32\nsimple depiction of the underlying mechanism and the nature of the optical transition\nwould help.”\nResponse:\nWe sincerely thank the Referee for this helpful suggestion. THz low-energy photon\ndetection is exclusively mediated by free-carrier intra-band transitions in materials,\nwhere photon absorption occurs without inter-band excitation. The free-carrier\nabsorption represents the dominant mechanism for intra-band electronic transitions in\noptical absorption, characterized by carrier excitation from lower to higher energy\nstates within a single valley of the band structure.\nThe Free-carrier absorption coefficient for THz photon detection, as established in\nprior studies1,2, exhibits a nonlinear dependence on relaxation time (τ) and incident\nphoton frequency (ω), governed by the following relation:\n𝑛𝑒2 1 1\n𝛼(𝜆) = 〈 〉\n𝜂𝑐𝑚∗𝜀 𝜔2 𝜏\n0\n𝛼(𝜆) represents the free-carrier absorption coefficient, 𝑛 represents the free\ncarrier concentration, 𝜂 stands for the refractive index, 𝑐 denotes the speed of light\nin vacuum, 𝑚∗ denotes the effective mass, and 𝜀 stands for the permittivity constant.\nincident light wavelength. This relationship demonstrates that the response of THz\ndetection gradually decreases as the frequency increases.\nThe limited output power of THz sources poses a significant technical challenge\nin THz detection. Commercially available THz systems show a gradual decline in\nsource power as frequency increases, leading to experimentally observed reductions in\nphotoresponse at higher frequencies. This power-frequency correlation directly\nexplains the diminished photoresponse observed in experimental results.\n1. Pankove J I. Optical Processes in Semiconductors. Princeton Press, 1973\n2. Pidgeon C R. Free Carrer Optical Properties of Semiconductors. Vol. 2, M. Balkanski,\n223-328, North-Holland, Amsterdam, 1980\nWe sincerely thank the reviewer for this insightful suggestion. Based on the\nreviewer’s suggestion, we have provided a detailed discussion of this point in the\nSupplementary Information (Supplementary Note 8).\nComment 9):\n“For readers not familiar with heterodyne mixing techniques, a simplified\nexplanation of the measurements shown in Figure 4 would be helpful.”\n10 / 32\nResponse:\nWe sincerely appreciate the reviewer's suggestion to provide a more accessible\nexplanation of heterodyne mixing techniques for readers. We offer a simplified\ndescription that is incorporated into the revised manuscript (Methods section).\n“A heterodyne is a signal frequency that is created by combining or mixing two other\nfrequencies using a signal processing technique called heterodyning, which was\ninvented by Canadian inventor-engineer Reginald Fessenden. Heterodyne mixing can\nbe understood by analogy to musical beats - when two slightly different musical notes\nare played simultaneously, we hear a pulsating 'beat' at the difference frequency\nbetween them. Similarly, in heterodyne mixing, two signals at different frequencies\n(local oscillator and radio frequency) are combined in a nonlinear device (the mixer),\nproducing new signals at the sum (f + f ) and difference (|f - f |) frequencies. In\nRF LO RF LO\nour measurements, the fabricated mixer (kagome material-based detector) serves as a\nfrequency conversion device circuit (Fig. 4a), which constitutes a critical component in\nmodern RF communication systems. The differential frequency (referred to as the\nintermediate frequency) is selectively utilized because it enables easier electronic\nprocessing compared to the original high-frequency signal.” (Page 14-15, Lines 420-432)\n———— R E P L Y T O R E V I E W E R 2 ————\nReviewer #2 (Remarks to the Author):\n“The authors explained the optoelectronic response of RVS in terms of charge\ndensity waves and VHS. All experimental data look clear, but there are many unclear\ndescriptions in the manuscript. Even though the manuscript shows good data on\noptoelectronic properties related to the CDW gap, I am sorry that I cannot recommend\nthe current manuscript for publication in Nature Communications.”\nResponse:\nWe are deeply grateful for your constructive feedback on our manuscript. We\nsincerely thank you for acknowledging the clarity and quality of our experimental data.\nWe sincerely apologize for the lack of clarity in our original descriptions, which\nevidently obscured the strengths of our work. Your insights have been invaluable in\nguiding the improvements we have made to address the concerns raised, particularly\nthe writing style of the manuscript. We have revised the introduction and descriptions\nof experimental results throughout the manuscript to ensure a clearer presentation of\nthe experimental data. In the following paragraphs, we will address each of the\nreviewer’s comments point by point. We hope that our responses and revisions meet\n11 / 32\nyour expectations.\nMajor comment 1:\n“I cannot understand why the authors are emphasizing Moiré superlattices in the\nmanuscript. The experiments are not directly connected with Moire physics (CDW) and\nFermi surface nesting. Please explain the clear reason why the authors can connect the\ncurrent work with Moiré physics.”\nResponse:\nWe gratefully acknowledge the reviewers' insightful comments and fully concur\nwith their valuable suggestions. We acknowledge that the emphasis on \"Moiré physics\"\nin our original manuscript may have been misleading, as our work primarily focuses on\nthe fundamental aspects of CDW formation and Fermi surface nesting in the kagome\nsystem. The use of \"Moiré\" was primarily because “practical deployment of moiré\nsystems in photoelectric conversion remains constrained by inherent fabrication\nlimitations. Current strategies primarily employ mechanical stacking8 or CVD\ntechniques9.” Specifically, the mention of Moiré superlattices in the introduction aims\nto highlight VHS as a feasible approach for engineering photoresponse properties.\nHowever, inherent challenges in the fabrication of Moiré superlattices presently limit\ntheir viability in photodetector applications. To circumvent these limitations, we turn to\nkagome lattice materials, which host intrinsic VHS. Our study investigates this\nalternative platform to explore new pathways for developing photodetectors based on\nkagome materials.\nWe agree that the direct connection to the contemporary context of Moiré physics\nin twisted bilayer graphene is not strong. Consequently, we have revised the\nintroduction to “While VHS near the E can be achieved through Graphene-based\nF\nMoiré superlattices16,17. Current fabrication strategies for advanced optoelectronic\ndevices18,1, which rely heavily on mechanical stacking20 and CVD techniques21, face\nsignificant limitations that hinder the development of robust and scalable applications.”\nBased on your insightful comments, we thoroughly scrutinize the entire\nmanuscript and revise the issues such as unclear language. Furthermore, we have\nrevised the Introduction section to clarify the focus on the geometric dislocation lattice\nsystem and the detection of CDW phase transitions. The modified Introduction is also\nhighlighted in red font for reference.\n“The geometrically frustrated lattice, a network of corner-sharing triangles1, represents\na foundational platform in condensed matter physics for hosting a spectrum of exotic\nquantum states2-4. It normally causes Fermi surface reconstruction coupled with\n12 / 32\nsingularities in the electronic band structure at the Fermi level (E )5. These diverse\nF\nquantum states include , charge density wave (CDW)6, spin-liquid states7, orbital\nmagnetism8,9, pair density wave (PDW)10, and unconventional superconductivity11,12.\nVan Hove singularities (VHS) can drive diverse quantum phenomena13,14; however,\ntheir implications for responses to different types of electromagnetic probes (e.g., light)\nremain underexplored15. VHS near the E can be achieved through Graphene-based\nF\nMoiré superlattices16,17. Current fabrication strategies for advanced optoelectronic\ndevices18,19, which rely heavily on mechanical stacking20 and CVD techniques21, face\nsignificant limitations that hinder the development of robust and scalable applications.\nIn contrast, VHS can naturally occur in kagome lattices22,23, providing a compelling\nalternative platform. By harnessing VHS-dominated optoelectronic transitions24,25,\nsuch platforms offer a viable pathway for next-generation quantum applications.” (Page\n2, Lines 46-60)\nMajor comment 2:\n“I can agree on the explanation for VHS1 and VHS2. But VHS3 is not. In the case\nof VHS1 and VHS2, the author's claim is valid because the points are located at the M\npoint (Brillouin zone boundary). However, VHS3 is hard to claim as the saddle point,\neven though it is valid to explain as the singularity point for the density of states. It\nlooks good to explain by the formation of CDW gap.”\nResponse:\nWe sincerely appreciate the Referee’s careful review and thoughtful comments.\nFrom Figs. R4a,b, we can ascertain that the VHS originates from the opening of the\nCDW gap, rather than a global downward shift of the bands. Even though the band\nstructure above the E cannot be displayed in our ARPES results, our findings still\nF\nsupport the conclusion of CDW gap opening. Specifically, in Fig. R4c, the yellow-\nmarked VHS3 does not extend into the Γ-M region, which is consistent with the\ncalculated results in Figs. R4a,b.\nThrough careful identification, we demonstrate the existence of saddle points in\nFig. R4d and Fig. R4f—a hole pocket along the M direction and an electron pocket\nalong the R direction—which aligns with related works (PhysRevLett.127.236401).\nThe presence of VHS3 remains fundamental to the subsequent discussion. We thank the\nreviewer for their comments; we have revised the description in the original manuscript\nfor clearer expression.\n13 / 32\nRevised Figure R4 a,b (Fig. S5) Calculated DFT band structures of the CDW phase along high-\nsymmetry directions in the Brillouin zone are shown for two cases: (a) without SOC and (b) with\nSOC. c (Fig. 2h) Second derivative spectrum along the high-symmetry path M-K-Γ at 10.5 K (below\nT ). The dotted line enhances the visibility of the energy bands near the M point, clearly revealing\nCDW\nthe band structure around VHS1 and VHS3. d (Fig. S4b) Calculated CDW state and corresponding\nARPES intensity plot along the M-VHS3-R direction, with yellow dashed lines serving as guides\nto the eye. e (Fig. 2i) Experimental and theoretical Fermi surface comparison. Orange markers\n14 / 32\nindicating the R direction. f (Fig. 2j) ARPES spectra from the momentum-space trajectories (cuts\n1-5) in Fig. 2i as indicated by grey lines. The yellow dashed line highlights the electron-like band,\nwhile the green dashed line indicates the hole-like band. The arrows in cut 3 indicate the appearance\nof VHS3.\nMajor comment 3:\n“The authors emphasized \"62-fold\" in the abstract and introduction, but there is\nno explanation.”\nResponse:\nWe sincerely appreciate the reviewer's comment regarding the emphasis on the\n'62-fold enhancement' in our abstract and introduction. In the original manuscript, the\nphotoresponse enhancement ratio, measured from the kagome-based device before and\nafter phase transition, quantifies a significant photoelectric enhancement factor (61.81×\n(0.03 THz)). It can be estimated by 𝐼 ⁄𝐼 (𝐼 is the 𝐼 measured in\n𝐶𝐷𝑊 𝑛𝑜𝑟𝑚𝑎𝑙 𝐶𝐷𝑊 𝑝ℎ\nCDW state and 𝐼 is the 𝐼 measured in normal state). We fabricated a new\n𝑛𝑜𝑟𝑚𝑎𝑙 𝑝ℎ\ndevice to validate our experiment and measured a photocurrent gain of 60.82 (× 0.03\nTHz), which confirms the initial result.\nWe provide a detailed qualitative analysis of the experimentally observed\nphotoresponse enhancement to elucidate the unique physical phenomena exhibited by\nkagome-based material devices. We address this question from the following three\naspects:\n1). THz detection in kagome systems primarily arises from intra-band transitions, with\nphotocurrent density showing a strong positive correlation with the DOS near the E .\nF\nTHz low-energy photon detection is exclusively mediated by free-carrier intra-\nband transitions in materials, where photon absorption occurs without inter-band\nexcitation. The free-carrier absorption represents the dominant mechanism for intra-\nband electronic transitions in optical absorption, characterized by carrier excitation\nfrom lower to higher energy states within a single valley of the band structure.\nThe Free-carrier absorption coefficient for THz photon detection, as established in\nprior studies1,2, exhibits a nonlinear dependence on relaxation time (τ) and incident\nphoton frequency (ω), governed by the following relation:\n𝑛𝑒2 1 1\n𝛼(𝜆) = 〈 〉. (1)\n𝜂𝑐𝑚∗𝜀0𝜔2 𝜏\n𝛼(𝜆) represents the free-carrier absorption coefficient, 𝑛 represents the free\ncarrier concentration, 𝜂 stands for the refractive index, 𝑐 denotes the speed of light\nin vacuum, 𝑚∗ denotes the effective mass, and 𝜀 stands for the permittivity constant.\n0\n15 / 32\nThe free-carrier absorption coefficient is directly proportional to the square of the\nincident light wavelength. This relationship demonstrates that the response of THz\ndetection gradually decreases as the frequency increases.\nOn the other hand, the observed photoresponse aligns qualitatively with the\ntheoretical model in the original manuscript, which posits a positive correlation\nbetween photocurrent intensity and DOS. This alignment is clearly demonstrated by\ncomparing the photoresponse characteristics before and after the phase transition (Fig.\nR5).\nRevised Figure R5 (Fig. 3h) Comparison of photocurrent intensity between the normal phase and\nCDW phase.\n1. Pankove J I. Optical Processes in Semiconductors. Princeton Press, 1973\n2. Pidgeon C R. Free Carrer Optical Properties of Semiconductors. Vol. 2, M. Balkanski,\n223-328, North-Holland, Amsterdam, 1980\n2). The electric field coupling efficiency of THz antennas varies across frequency bands,\ndemonstrating stronger coupling in the low-frequency regime.\nThe coupling efficiency of THz antennas exhibits significant frequency\ndependence, with optimal performance achieved in the low-frequency regime. As\nshown in Fig. R6, the FDTD analysis of the THz field-enhancing antenna reveals a\nstrong electric field concentration near the channel, accompanied by a centrosymmetric\noptical distribution. Moreover, the simulations indicate a gradual decline in electric\nfield intensity with increasing frequency.\n16 / 32\nRevised Figure R6 (Fig. S7) a-d The electric field distribution of the bowtie antenna at (a) 0.02\nTHz, (b) 0.1 THz, and (c) 0.3 THz, along with (d) the field intensity profile along the X-axis.\n3). The reduced output power of THz sources at high frequencies, constituting a\nsecondary constraint.\nThe limited output power of THz sources poses a significant technical challenge\nin THz detection. Commercially available THz systems show a gradual decline in\nsource power as frequency increases, leading to experimentally observed reductions in\nphotoresponse at higher frequencies. This power-frequency correlation directly\nexplains the diminished photoresponse observed in experimental results.\nIn response to the issues, we performed a systematic comparison of device R\nA\nfollowing THz source power normalization (Fig. R7). Our measurements reveal a\npronounced enhancement in photoresponsivity during the CDW phase, exhibiting an\nincrease relative to the normal phase. Additionally, we have revised the relevant\ndescriptions in the original manuscript to ensure more precise and appropriate\nterminology alignment.\n17 / 32\nRevised Figure R7.The spectral responsivity as a function of frequency across the 0.02-0.34 THz\nrange, with distinct characteristics observed in both the normal phase and CDW phase.\nWe are grateful to the reviewer for this constructive suggestion, which has\nstrengthened the clarity and precision of our photoelectric detection analysis.\nMinor comment 1:\n“(line 110) Electron pockets at Gamma are not shown in Figure 1 (b), but are\nshown in (f). So I think it is not proper.”\nResponse:\nWe thank reviewer for the carefully reading and thoughtful suggestion. We\nsincerely regret any potential confusion arising from our initial imprecise expression.\nWe have revised the description of kagome materials' fundamental properties. Within\nthe conventional band structure framework, these systems consistently exhibit\ncharacteristic Dirac points.\n“Building upon prior research on kagome systems34, Figs. 1b,c illustrate three key\nelectronic band features of an ideal kagome lattice at normal state: (i) Dirac cones at\nthe K point, (ii) VHS at the M point, and (iii) momentum-space flat bands.” (Page 3-4,\nLines 98-101)\nMinor comment 2:\n“(line 85) What is the meaning and role of \"symmetry-engineered electrodes\"?”\nResponse:\nThanks again for the carefully reading and valuable comment. THz antennas are\nessential components of THz detection systems. In this study, we utilize a butterfly-\n18 / 32\nshaped, bilaterally symmetric antenna design that couples the THz optical field without\nintroducing structural asymmetry (Light: Science & Applications (2022) 11:53). This\napproach ensures that observed phenomena are solely attributable to the intrinsic\nsingular properties of the material under investigation. As demonstrated by the finite-\ndifference time-domain (FDTD) simulations in Fig. R6 (Fig. S7), the antenna exhibits\nidentical THz electric field gain on both sides, further validating its symmetric\nperformance.\n———— R E P L Y T O R E V I E W E R 3 ————\nReviewer #3 (Remarks to the Author):\n“The authors explore the possibility of utilizing the Fermi surface reconstruction\nassociated with charge-density wave transitions in 2D van-der-Waals materials -\nspecifically in the V-based kagome metal RbV3Sb5 - for photo-sensoric devices.\nVia ARPES and DFT calculations, they recall and highlight the temperature-dependent\nchanges in the electronic band structure, with an emphasis on a van-Hove singularity\nclose to the Fermi level. Exploiting these Fermi-surface features, they demonstrate a\nphotocurrent detection capabilities of a RbV Sb -based detector device. While this work\n3 5\ntackles an underexplored aspect of kagome metals which may open the door to future\napplications, there are several issues that deserve attention, clarification, and\nimprovement before considering the manuscript for publication.”\nResponse:\nWe sincerely appreciate the reviewer's insightful comments regarding the novelty\nand technical clarity of our study. We highly appreciate your recognition of our work’s\nsignificance in exploring an underexplored aspect of kagome metals and its potential to\nopen new avenues for future applications. We also take seriously the issues that require\nattention, clarification, and improvement, and have carefully addressed them to\nenhance the quality of our work. We have meticulously addressed each constructive\nsuggestion through comprehensive revisions and rewriting.\nComment 1:\n“The authors assume an inverse-Star-of-David as the CDW pattern in RbV3Sb5.\nAs far as I understand, the precise pattern is still an open issue (although recent works\nseem to slightly favor an inverse-Star-of-David over a star-of-David pattern). Can the\nauthors elaborate on their assumption? I suggest they also plot the electronic band\nstructure for a star-of-David pattern for comparison and comment on the fundamental\ndifferences between those two (if any).”\nResponse:\n19 / 32\nWe sincerely thank the reviewer for this evaluable suggestion. We agree that the\nprecise pattern is still an open issue, especially recently reported MLL pattern of CDW,\nwhich shows bilayer configuration with a π shift between layers (Nature Materials 22\n186-193 (2023)).\nWhile the precise pattern exhibits considerable complexity and lies beyond the\nprimary scope of this study, we refrain from extensive commentary on this aspect.\nInstead, we direct our analysis toward elucidating the key distinctions between the\ninverse-Star-of-David (ISD) and Star-of-David (SD) configurations, as previously\nmentioned in this work.\nWe first started with the phonon spectrum of the pristine structure, revealing\nimaginary frequencies at the M and L points. This indicates that the high-temperature\nparent phase is structurally unstable. To explore this further, we introduced distortions\nbased on a 221 supercell and leveraged the accuracy of density functional theory\n(DFT) in computing ground-state energies. We identified two local minima with lower\nground-state energies compared to the pristine structure, corresponding to the SD and\nISD distorted configurations, which is shown below. Notably, the ISD configuration\nwas found to have the global minimum ground-state energy.\nFurthermore, we calculated the unfolded Fermi surface and band structure for\npristine, ISD and SD phase to elucidate the changes in electronic structure relative to\ndifferent CDW patterns. By comparing Revised Figure R9 b and a (Extended Data\nFig. 1), we observed that the ISD Fermi surface exhibits a discontinuity along the M-\nto-K direction (highlighted in the red box), suggesting the presence of a gap. Similarly,\na comparison between Revised Figure R9 c (red box) and reveals significant changes\nat the M point. Moreover, we analyzed the band dispersions along high-symmetry paths\nfor all three structures. In the Г-K direction, both ISD and SD configurations exhibit a\nlarger gap compared to the pristine structure (indicated in the blue box). Additionally,\nthe ISD configuration displays a splitting of the VHS at the M point, with a pronounced\nspectral weight above the E . While this splitting is also present in the SD configuration,\nF\nthe spectral weight above the E is considerably less prominent. Moreover, in the ISD\nF\nconfiguration, the VHS at the L point is shifted to lower energy relative to the pristine\nstructure (red box), whereas the SD configuration shows minimal energy shift, closely\nresembling the pristine structure. Note here that the calculated fermi level has 0.1 eV\nshifting compared to experiment observation and we label the experiment fermi energy\non every band structure.\n20 / 32\nRevised Figure R8. Total energy profiles for the RVS. The distortion stands for the amplitude of\nthe breathing-phonon mode where the negative values are used for SD in order to distinguish from\nISD. The Energy stands for the total energy of each supercell (36 atoms).\nRevised Figure R9. The Normal-phase (a), ISD CDW-phase (b)and SD-CDW-phase (c) FS sheets\nare displayed at 𝑘 =0, where the spectral function A (k, E ) is drawn using the color scale. The\n𝑧 F\ncalculated spectral function for the normal (d), ISD CDW (e) and SD CDW (f) phase unfolded to\nthe pristine BZ\nComment 2:\n“Related to the former comment is the issue of potential stacking faults, which are\nknown to occur in V-based kagome materials depending on the cleavage procedure as\n21 / 32\nwell as the cooling rate. The authors should discuss these potential effects, as they may\nbe highly relevant for future fabrication and application processes.”\nResponse:\nWe appreciate the reviewer's insightful suggestion regarding stacking faults in V-\nbased kagome materials. This is indeed an important consideration for both\nfundamental understanding and practical applications. Based on our analysis, we\nconfirm that this does not affect the conclusions of our study. The detailed discussion\nproceeds as follows:\nStacking faults are local changes in the stacking sequence. Previous studies have\ndemonstrated analogous stacking effects in KV₃Sb₅ and CsV₃Sb₅ (PhysRevLett 132,\n066501 (2024)), confirming this as a universal feature of the AV₃Sb₅ family. Specifically,\nwhen a 2×2 reconstruction of A-site atoms (A = Cs, Rb, K) occurs on the surface of\nKagome materials, a π-phase-shifted stacking fault—manifesting as a phase-twisted\ndefect—emerges if the surface phase deviates from the bulk CDW order. Our\ninvestigation centers on the enhanced photoresponse of kagome materials for low-\nenergy photon detection following phase transitions, a phenomenon governed by\nintrinsic electronic properties. Crucially, neither ARPES data nor device performance\nmetrics show any measurable influence from surface-localized stacking faults. This\nrobust insensitivity demonstrates that structural defects introduced through mechanical\nexfoliation or non-equilibrium cooling protocols do not affect the conclusions of our\nstudy.\nWe agree with the reviewer that this is a crucial point. A detailed exploration of\nthis aspect is indeed necessary, and we plan to address it in our future work. Systematic\ninvestigations using scanning tunneling microscopy (STM) have recently revealed\nsingular electronic phenomena originating from stacking faults (Nature\nNanotechnology 20, 1017–1025 (2025)). Their work on an artificially engineered 2×2\nCs-ordered surface demonstrates the emergence of quasi-two-dimensional\nsuperconductivity concomitant with a pair density wave (PDW). This atomically\nprecise control over stacking defects provides a novel platform for engineering quantum\nmany-body states.\n“Recent investigations have revealed that stacking faults in kagome metals generate a\ndistinct electronic environment through phase-twisted termination configurations1.\nThis unique environment facilitates the emergence of localized surface states, enhances\nsuperconductivity, and promotes the formation of an unconventional pair density wave\n(PDW) order. These atomically precise stacking defects establish a novel pathway for\nengineering quantum many-body states.” (SI Page 4, Lines 88-93)\n22 / 32\nComment 3:\n“In Fig. 2a, the resistivity curves from three different samples show transition\ntemperatures between 92 K and 102 K. Meanwhile, the authors emphasize an\n\"outstanding single-crystal quality\". Please discuss in the manuscript the potential\norigin of the wide range of transition temperatures.”\nResponse:\nWe sincerely appreciate the reviewer's insightful observation regarding the\ntransition temperature range in our single-crystal samples. This is indeed an important\npoint that warrants discussion in the manuscript.\nIn response to this comment, we have (i) performed temperature-dependent\nresistance measurements on samples with varying thicknesses and (ii) expanded the\ndiscussion on phase transition temperature variations in Figure 2.\nThe original resistivity test results (original Figure 2a) were obtained from samples\nwith varying mechanical exfoliation thicknesses, exhibiting differences in transition\ntemperatures. Notably, these devices were all fabricated using materials with\nexceptional single-crystal quality.\nBuilding upon previous discussions in related studies (Nature Communications 14\n2492 (2023)), we have confirmed that reducing sample thickness can induce changes\nin the critical temperature. The Revised Figure R10 presents temperature-dependent\nresistance measurements across samples of varying thicknesses. While the minimum\nachieved thickness (94 nm) remains above the 2D limit (<10 nm), these \"thick\" samples\nstill exhibit thickness-dependent phenomena.\nRevised Figure R10. a Atomic force microscopy (AFM) analysis of the RVS sample reveals a\nconsistent thickness of approximately 129 nm, as measured along the trajectory indicated by the\n23 / 32\nsolid red line. b Temperature dependence of the resistance for RVS thin flakes with various thickness.\nThe curves are vertically shifted for clarity. The arrows mark the CDW transition temperature T .\nCDW\n“As established in prior investigations36, the T exhibits pronounced thickness\nCDW\ndependence in AVS materials. Our systematic study employs ~ 140-nm-thick sample—\na dimensionality carefully selected to maintain bulk-like electronic properties while\navoiding the 3D-to-2D crossover regime.” (Page 4-5, Lines 126-129)\nComment 4:\n“The authors also speculate about softening of acoustic modes \"possibly\nevidencing a structural instability\" - there have been numerous studies detailing el-el\nand el-ph coupling, and the role of crystal structure on the CDW formation AV3Sb5, so\nI don't get why the authors need to describe it in these vague terms. Better to add some\nrelevant references at this point.”\nResponse:\nWe appreciate the reviewer's constructive suggestions regarding the description of\nacoustic mode softening in our manuscript. The kagome material AV₃Sb₅ provides an\nideal platform for investigating electronic correlations, with electron-phonon coupling\nplaying a critical role in its phase transition behavior. As noted by reviewers, recent\nstudies on the AV₃Sb₅ family reveal that in systems exhibiting Fermi surface nesting—\nwhere parallel segments of the Fermi surface share a common wavevector in\nmomentum space—electron-phonon coupling typically drives periodic lattice\ndistortions. This mechanism induces band splitting (i.e., a CDW gap opening at the E ),\nF\nthereby stabilizing the system through a reduction in ground-state energy.\nSupporting this, our phonon dispersion calculations (Fig. 2b) identify soft phonon\nmodes at the M and L points, confirming the dynamical instability of the pristine lattice.\nThese soft modes mediate the phase transition, favoring the ISD structure over the SD\nstructure due to its lower energy and enhanced stability.\nThe manuscript has been revised accordingly to these suggestions.\n“Additionally, our finding reveals that the pristine phase demonstrates marked\nstructural instability. Our frozen-phonon calculations performed on a 3×3×1 supercell\nreveal significant phonon mode softening around the M and L points of the Brillouin\nzone (BZ) boundary in the RVS phonon dispersion (Fig. 2b), unambiguously indicating\ninherent structural instability in the pristine phase37,38. This lattice dynamical instability\nserves as the driving mechanism for the CDW phase transition.” (Page 5, Lines 130-135)\nComment 5:\n24 / 32\n“I find some of the phrasing related to the ARPES results somewhat confusing. I\nget that the authors want to present their ARPES results to link features of the electronic\nband structure to photo-sensoric activity of RbV3Sb5. However, in my view the\nelectronic (CDW) phase transition has been heavily studied and well-established for\nyears. Yet, parts of the text read as if nothing is known so far about the electronic\nstructure. Take for example: \"Compelling evidence of electronic phase transitions in\nKagome materials\". Am I missing some newly uncovered observation made by the\nauthors for the first time? Otherwise, these ARPES results do not report any novel\ndiscovery or observation, hence there is no need to present them as \"compelling\nevidence\".”\nResponse:\nWe sincerely appreciate the reviewer's insightful suggestion regarding the\nphrasing of our ARPES results. We agree that the electronic phase transitions in kagome\nmaterials have been extensively studied, and we acknowledge the need to clarify the\nnovelty of our observations in this context. We have adjusted the language of the\ndescription in that section to present the experimental results more clearly. The revised\nsection is in resvied manuscript (Singular Electronic Band Behavior in RbV₃Sb₅).\nWe thank the reviewer for prompting us to refine the presentation of our ARPES results.\nThese revisions have strengthened the manuscript by more precisely delineating\nestablished knowledge from our original contributions.\nThe word “Compelling evidence of electronic phase transitions in Kagome\nmaterials through combined ARPES and DFT investigations.” has been modified\nby “Experimental evidence of CDW formation in RVS and VHS signature from\nelectronic structure analysis.” (Page 23, Lines 595-596)\nComment 6:\n“Finally, I would like to see a comparison of the photo-sensoric performance of\nRbV3Sb5 with other related vdW materials, as well as with other, conventional\nmaterials in the discussion, so that the readers may better appreciate the performance.\nLikewise, can the authors comment on potentially utilizing other CDW materials with\na transition temperature closer to room temperature? Are there any fundamental\nadvantages of V-based kagome metals?”\nResponse:\nWe sincerely appreciate the reviewer's kind and helpful suggestions regarding the\nperformance benchmarking of RbV₃Sb₅ and the potential of CDW materials for room-\ntemperature applications. These points are crucial for contextualizing our work, and we\nhave expanded the discussion accordingly.\n25 / 32\n1. A comparison of photosensitive properties with other relevant vdW materials and\nconventional materials\nThe detector performance of topological semimetals (e.g., Dirac and Weyl\nsemimetals) within van der Waals (vdW) materials was systematically evaluated against\nconventional 2D materials, such as graphene and black phosphorus. This comparison\nfocused on two critical metrics: responsivity and noise-equivalent power (NEP). As\nillustrated in Figure S11 f, the results highlight the superior performance of topological\nsemimetals1–10. Notably, the THz photodetector fabricated using the RVS architecture\nexhibits exceptional detection capabilities, underscoring its potential for advanced\noptoelectronic applications.\nRevised Figure R11. (Fig. S11 f) The comparative performance evaluation between RVS detectors\nand conventional THz detection technologies.\nTopological materials (RVS) demonstrate a significant advantage in response time\ncompared to conventional materials. We systematically compared key metrics such as\ndetector response time between these material systems.\n26 / 32\nRevised Table 1. Detailed performance (Response time) specifications of common THz detectors\nNEP Response\nMaterial Responsivity Refs.\n(pW Hz-1/2) time\nBi Te Se 0.21 V W-1 13600 20 ms 11\n2 2.2 0.8\nT -MoTe 0.53 mA W-1 2650 26 μs 12\nd 2\nMoS 0.57 A W-1 - 70–110 µs 13\nRVS 11.26 A W-1 16.36 580 ns This work\n2. Potential of Other CDW Materials Near Room Temperature\n1) TiSe₂:\nARPES and first-principles calculations reveal that bulk TiSe₂ undergoes a CDW\ntransition at 200 K. This work also identifies its narrow-bandgap semiconductor\ncharacteristics (bandgap ≈98 meV) and electronic band reconstruction15,16.\nIn a complementary study, simulations of a TiSe₂-based photodetector\ndemonstrated a photoresponsivity of 0.67 A/W at 920 nm, limited by the material’s low\ncarrier mobility17.\n2) CuTe:\nCuTe exhibits a CDW transition temperature of 300 K under hydrostatic pressure\n(6.5 GPa). While this temperature approaches room-temperature operability, the\nnecessity for sustained high-pressure conditions poses challenges for practical detector\nintegration, including increased energy consumption and engineering complexity18,19.\n3) TaS₂:\nTaS₂ exhibits characteristic CDW sliding behavior, with a CDW transition\noccurring near room temperature (~350 K for the nearly commensurate (NC) phase).\nWhen an external electric field surpasses the threshold for phase excitation modes, the\nmaterial displays pronounced nonlinear current-voltage characteristics, marked by an\nabrupt resistance drop—a signature of collective CDW depinning.\nNotably, sub-threshold optical excitation can modulate the resistive state even\nwhen the applied bias voltage is insufficient to trigger CDW sliding. This effect induces\npremature phase-mode sliding, suggesting a light-sensitive control mechanism for\nCDW dynamics. Such behavior enables applications in broadband photodetection,\nwhere the RVS mechanism exploits TaS₂’s intrinsic coupling between electronic and\nstructural orders for optoelectronic response20.\n3.Fundamental Advantages of V-Based Kagome Metals\n1) Unique Electronic Properties Arising from the Structure of Vanadium-Based\nKagome Metals\nThe vanadium-based kagome metals, particularly the AV₃Sb₅ (A = K, Rb, Cs)\nfamily, have emerged as an exceptional platform for investigating the interplay of\ngeometric frustration, electronic correlations, and topological states in quantum\nmaterials. The two-dimensional kagome lattice—composed of corner-sharing\ntriangles—generates several extraordinary electronic features21:\n(1) Dirac Points:\nSimilar to graphene, the kagome lattice inherently possesses Dirac cones in its\nband structure. However, due to the involvement of a three-orbital basis, these cones\nexhibit more complex characteristics\n(2) Flat Bands:\nThe strong geometric frustration in the kagome lattice gives rise to completely\ndispersionless (flat) electronic bands, significantly enhancing electron correlation\neffects.\n(3) VHS:\nA high density-of-states point in electronic structures induced by lattice geometry,\ncapable of driving various instabilities.\n2) Rich Phase Diagrams with Coexisting Multiple Order Parameters\nVanadium-based kagome metals exhibit exceptionally rich phase diagrams\nencompassing multiple competing electronic ordered states:\n(1) CDW:\nThese materials exhibit a CDW transition at relatively high temperatures\n(approximately 70–100 K, depending on the A-site element), which is highly unusual\nin metallic systems22.\n(2) Time-Reversal Symmetry Breaking:\nScanning tunneling microscopy (STM) and muon spin relaxation (μSR)\nexperiments reveal time-reversal symmetry breaking below the CDW transition\ntemperature, suggesting the possible existence of a chiral flux phase or orbital currents23.\n(3) Electronic Nematic Phase:\nBelow the CDW transition temperature, these materials form an electronic nematic\n28 / 32\nphase that breaks the sixfold rotational symmetry of the kagome lattice.\n3) Topologically Nontrivial Unconventional Superconductivity\n(1) Strong Coupling:\nThe ratio of 2Δ/kBTc ≈ 5 in CsV₃Sb₅ indicates that it belongs to the category of\nstrongly coupled superconductors24.\n(2) Pair Density Wave (PDW):\nHigh-resolution scanning tunneling microscopy (STM) has revealed a 3Q PDW\nstate coexisting with superconductivity in CsV₃Sb₅, manifested as spatial modulation\nof the superconducting gap. This \"roton-PDW\" state may be associated with an\nunderlying vortex-antivortex lattice.\n(3) Topological Aspects:\nThe combination of nontrivial band topology and superconductivity may endow\nthese materials with topological superconducting properties25.\n1. Qin, H. et al. Room-temperature, low-impedance and high-sensitivity terahertz direct\ndetector based on bilayer graphene field-effect transistor. Carbon 116, 760–765 (2017).\n2. Zak, A. et al. Antenna-integrated 0.6 THz FET direct detectors based on CVD graphene.\nNano Lett. 14, 5834–5838 (2014).\n3. Guo, W. et al. Sensitive terahertz detection and imaging driven by the photothermoelectric\neffect in ultrashort‐channel black phosphorus devices. Advanced Science 7, 1902699\n(2020).\n4. Wang, L. et al. Hybrid dirac semimetal-based photodetector with efficient low-energy\nphoton harvesting. Light Sci Appl 11, 53 (2022).\n5. Dong, Z. et al. Highly Efficient, Ultrabroad PdSe Phototransistors from Visible to\n6. Zhang, L. et al. High-frequency rectifiers based on type-II Dirac fermions. Nat. Commun.\n12, 1584 (2021).\n29 / 32\n7. Xu, H. et al. PtTe2-based type-II dirac semimetal and its van der waals heterostructure for\nsensitive room temperature terahertz photodetection. Small 15, 1903362 (2019).\n8. Yang, L. et al. Low-power polarization sensitive terahertz photodetection driven by ternary\ntype-II weyl semimetal NbIrTe . IEEE Electron Device Lett. 44, 686–689 (2023).\n4\n9. Zhang, L. et al. Ultrasensitive and Self‐Powered Terahertz Detection Driven by Nodal‐\nLine Dirac Fermions and Van der Waals Architecture. Advanced Science 8, 2102088\n(2021).\n10. Guo, C. et al. Ultrasensitive Anisotropic Room-Temperature Terahertz Photodetector\nBased on an Intrinsic Magnetic Topological Insulator MnBi Te . Nano Lett. 22, 7492–\n2 4\n7498 (2022).\n11. Viti, L. et al. Plasma-wave terahertz detection mediated by topological insulators surface\nstates. Nano Lett. 16, 80–87 (2016).\n12. Yang, Q. et al. A centimeter‐scale type‐II weyl semimetal for flexible and fast ultra‐\nbroadband photodetection from ultraviolet to sub‐millimeter wave regime. Advanced\nScience 10, 2205609 (2023).\n13. Tsai, D.-S. et al. Few-layer MoS2 with high broadband photogain and fast optical\nswitching for use in harsh environments. ACS Nano 7, 3905–3911 (2013).\n14. Hu, P., Wen, Z., Wang, L., Tan, P. & Xiao, K. Synthesis of few-layer GaSe nanosheets for\nhigh performance photodetectors. ACS Nano 6, 5988–5994 (2012).\n15. Chen, P. et al. Charge density wave transition in single-layer titanium diselenide. Nat\nCommun 6, 8943 (2015).\n16. Song, Z. et al. Observation of an incommensurate charge density wave in monolayer\n30 / 32\nTiSe 2 / CuSe / cu ( 1 1 1 ) heterostructure. Phys. Rev. Lett. 128, 026401 (2022).\n17. Miah, Md. R., Ebon, Md. I. R., Abir, A. T. & Hossain, J. Modeling and numerical\ninsights of TiSe compound‐based photodetector. Advcd Theory and Sims 7, 2400389\n2\n(2024).\n18. Shi, Y. et al. Concurrence of in-plane anisotropic superconductivity and quasi-one-\ndimensional charge density wave in layered CuTe under high pressure. Phys. Rev. B 111,\nL180507 (2025).\n19. Wang, S. et al. Two distinct charge density wave orders and emergent superconductivity\nin pressurized CuTe. Matter 6, 3526–3537 (2023).\n20. Wu, D. et al. Ultrabroadband photosensitivity from visible to terahertz at room\ntemperature. Sci. Adv. 4, eaao3057 (2018).\n21. Wang, Y., Wu, H., McCandless, G. T., Chan, J. Y. & Ali, M. N. Quantum states and\nintertwining phases in kagome materials. Nat Rev Phys 5, 635–658 (2023).\n22. Cho, S. et al. Emergence of New van Hove Singularities in the Charge Density Wave\nState of a Topological Kagome Metal RbV 3 Sb 5. Phys. Rev. Lett. 127, 236401 (2021).\n23. Xing, Y. et al. Optical manipulation of the charge-density-wave state in RbV3Sb5.\nNature 631, 60–66 (2024).\n24. Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor.\nNature 599, 222–228 (2021).\n25. Luo, H. et al. Electronic nature of charge density wave and electron-phonon coupling in\nkagome superconductor KV3Sb5. Nat Commun 13, 273 (2022).\n31 / 32\nMinor issues 1-3:\n1. Abstract: \"enhancement in in terahertz\"\n2. Line 45: Add a reference at the end of the first sentence.\n3. Line 47: Ref. 1 does not seem to be a proper, primary reference here.\nResponse:\nWe appreciate the reviewer’s valuable comment. Following the reviewers'\nsuggestions, I have revised the “Introduction” section of the manuscript, modifying\nthe corresponding text and adding relevant cited references.\nMinor issues 4-6:\n4. Line 106: specify the value of T_CDW, add a reference at the end of the sentence.\n5. \"Notably, upon entering the CDW phase (T < T ), the VHS near the M point\nCDW\nprogressively shifts away from the EF, while a new VHS forms at the R point.\": mark\nand illustrate these changes in Fig. 1 as well.\n6. Lines 241-243 and lines 249-250 are nearly identical.\nResponse:\nWe appreciate the reviewer’s valuable comment. In response to the reviewers'\ncomments, we have revised the VHS3-related sections of the manuscript.\n“RVS undergoes a CDW phase transition at T (~102 K)33, accompanied by\nCDW\nsubstantial electronic band structure reconstruction.” (Page 3-4, Lines 98-99)\n“Notably, upon entering the CDW phase (T < T ), the VHS near the M point\nCDW\nprogressively shifts away from the E (Extended Data Fig. 2).” (Page 4, Lines 112-114)\nF\nMinor issues 7:\n7. Since Fig. 3b only contains 5 curves, it might be advantageous to simply plot all\ncurves on top of each other to better appreciate the changes through the transition\ntemperature.\nResponse:\nWe appreciate the reviewer’s valuable comment. To further clarify the EDC\nchanges induced by VHS3, we have included additional EDC curves at the VHS3 point\nin Fig. 3b, where a newly appearing peak at low temperatures effectively reflects the\nemergence of the new VHS.\n32 / 32\n———— R E P L Y T O R E V I E W E R 1 ————\nReviewer #1 (Remarks to the Author):\n“I appreciate the authors’ efforts in addressing my comments and questions. A few\nmore points require clarification before I recommend the manuscript for publication:”\nResponse:\nWe are very grateful for the reviewer's overall positive assessment of our revisions\nand their continued engagement with our manuscript. We sincerely appreciate the\nopportunity to clarify the remaining points. Below we provide a point-by-point\nresponse to the additional comments.\nComment 1):\n“The authors provided DFT calculated CEC (Extended Data Fig. 1) to illustrate\nthe reported temperature depended Fermi surface reconstruction. However, I wonder\nhow do these compare with the CEC at the Fermi level measured with ARPES. Is the\nFermi surface reconstruction visible in the experimental data? If such data are\navailable, one could potentially plot a differential CEC (CEC 130K – CEC 10K).”\nResponse:\nWe sincerely thank the reviewer for raising this critical point and for proposing the\nhighly insightful differential CEC analysis. In response to reviewer’s suggestions, we\nconducted further analysis of the ARPES data. Our analytical findings are presented\nbelow:\nIn the original text, Fig. 2 displays high-resolution band dispersion measurements\nalong a high-symmetry direction at various temperatures. These results demonstrate\nclear band modifications when comparing the Pristine and ISD phases, with particular\nemphasis on the energy position of VHS3. This finding aligns with previous work (Phys.\nRev. Lett. 127, 236401). Our DFT calculation results clearly demonstrate the\nphenomenon of Fermi surface reconstruction. However, due to inherent limitations—\nsuch as the assumption in the calculations that the material is a perfect bulk at absolute\nzero—it is almost impossible for ARPES experimental results to completely reproduce\nthe DFT calculations. Furthermore,the ARPES analysis may be influenced by inherent\nexperimental limitations, such as, limited instrumental resolution, intrinsic thermal\nbroadening, and scattering from surface degradation.\nFollowing the reviewers' suggestions, we analyzed the CEC at the Fermi level (E\n= E ) for 130 K and 10.5 K (Fig. R1). Our experimental data exhibits subtle changes\nF\nbut the underlying electronic structure modification remains robust. Our experimental\nresults continue to support the core conclusion: the CDW phase transition induces\nsignificant band structure modifications.\nIn Fig. R2 a, the CEC measured at E= E −0.2 eV shows clear variations in spectral\nF\nintensity. Most notably, the density of states along the K–M–K (orange line segment)\ntrajectory is negligible at 130 K but becomes markedly enhanced at 10.5 K. This\ntemperature-dependent evolution is consistent with an electronic reconstruction driven\nby the CDW transition. We have included the Momentum Distribution Curve (MDC)\nalong the K−M−K direction in Figs. R2 a and b, where the spectral intensity at the\nVHS3 position is clearly enhanced at low temperatures. This strongly indicates that the\nband containing VHS3 shifts to lower energy at low temperatures, consistent with the\ncalculation results.\nFig. R3 presents thedifferential map of the E–k dispersion, revealing a pronounced\nintensity variation near the VHS3 feature. This observation confirms the downward\nenergy shift of the band hosting VHS3 at low temperatures. In Fig. R3c, the significant\ncolor difference within the boxed region indicates a clear energy shift of the electronic\nbands at different temperatures. In Fig. R4, we compare CECs at 10.5 K and 130 K\nacross multiple binding energies. Despite limitations in data quality, a discernible\ndifference induced by VHS3 is captured in the CEC at E= E −0.15 eV, as indicated by\nF\nthe yellow arrow. We thank the reviewer for this insightful suggestion, which has\nstrengthened our analysis.\nRevised Figure R1 Fermi surface (FS) mappings collected at 10.5 K (a) and 130 K (b).\nRevised Figure R2 constant energy contour plots at E= E −0.12 eV collected at 10.5 K (a) and\nF\nK and 130 K.\nRevised Figure R3(Supplementary Figure S4) ARPES spectra at 130 K (a) and 10.5 K (b) along\nthe M-K-Γ direction. c. The difference between spectra collected above and below T ; red (blue)\nCDW\ncorresponds to a negative (positive) difference.\nRevised Figure R4 Fermi surface and constant energy contour plots around the M point collected\nat 10.5 K (a) and 130 K (b). The constant energy contour plots at E= E −0.15 eV collected at 10.5\nF\nK (c) and 130 K (d).\nComment 2):\n“Similarly to above, the authors could extract a differential E-k map, where they\nsubtract the Extended Data Fig. 2e (10.5K) from Extended Data Fig. 2e (130K) (or\nthose from Fig. 2e and 2g). This will highlight newly formed bands (VHS3) that emerge\nupon CDW phase transition.\nMinor tip: proper photoemission intensity normalization will be needed before the\nsubtraction of the two spectra.”\nResponse:\nWe are grateful to the reviewer for this excellent suggestion. The differential E-k\nmap analysis is indeed a powerful method to visually highlight the subtle changes in\nthe electronic structure across the phase transition. We have performed this analysis as\nrecommended.\nFollowing the reviewer's suggestions, we subtracted the ARPES intensity map at\n10.5 K (T < T , Fig. 2g in the original manuscript) from that at 130 K (T > T ,\nCDW CDW\nFig. 2e). This differential map (E-k at 10.5K - E-k at 130K) is now presented as a new\nFigs. S4 c, d and e. Fig. R3e presents the differential map of the E–k dispersion,\nrevealing a pronounced intensity variation near the VHS3 feature. The significant color\ndifference within the boxed region indicates a clear energy shift of the electronic bands\nhosting VHS3 at different temperatures.\n“Fig. R3c and d display the difference in spectral intensity between data collected\nabove and below T , highlighting the redistribution of spectral weight. Red color\nCDW\ndenotes predominant low temperature features, while blue color is used for high\ntemperature. Fig. R3e presents the differential map of the E–k dispersion, revealing a\npronounced intensity variation near the VHS3 feature. The significant color difference\nwithin the boxed region indicates a clear energy shift of the electronic bands hosting\nVHS3 at different temperatures.” (SIPage 7, Lines 135-141)\nRevised Figure R3(Supplementary Figure S4) ARPES spectra at 130 K (a) and 10.5 K (b) along\nthe M-K-Γ direction. c. The difference between spectra collected above and below T ; red (blue)\nCDW\ncorresponds to a negative (positive) difference.\nComment 3):\n“Suggestion: My third comment is concerning the title of the manuscript. Maybe\nsomething like \"Photoresponse Enhancement upon Phase Transition-Induced Fermi\nSurface Reconstruction in Geometrically Frustrated Lattices\" would be more suitable,\nsince the enhanced photoresponse is a key finding of the manuscript.”\nResponse:\nWe sincerely thank the reviewer for this excellent and constructive suggestion\nregarding the manuscript title. We fully agree that the title should more prominently\nhighlight the key finding of our work—the substantial enhancement in photoresponse.\nThe proposed title, \"Photoresponse Enhancement upon Phase Transition-Induced\nFermi Surface Reconstruction in Geometrically Frustrated Lattices\", accurately\ncaptures the core narrative of our study.\nInspired by the reviewer's suggestion, we have refined the title to:\n“Harnessing Van Hove Singularities for Terahertz Photoresponse via Fermi\nSurface Reconstruction in Kagome Lattices”\n———— R E P L Y T O R E V I E W E R 2 ————\nReviewer #2 (Remarks to the Author):\n“The authors corrected the manuscript following the previous comments; now the\nlogics look concrete. I just have a minor suggestion; the others seem to be fine to publish\non Nature Communications.”\nResponse:\nWe would like to express our sincere gratitude for your time and valuable\ncomments on our manuscript. We are delighted to receive the positive feedback and\nhave carefully addressed the minor suggestion as detailed below. We believe the\nmanuscript has been further improved as a result.\nComment 1):\n“The colour of the capital 'VHS1' and 'VHS3' in Figure 2 (h) and (j) is hard to\nrecognize. It would be better to change for the reader's convenience.”\nResponse:\nWe sincerely thank the reviewer for pointing out the issue with the color contrast\nof the 'VHS1' and 'VHS3' labels in Figs 2h and 2j. We agree that improving the legibility\nof these labels is crucial for the reader's convenience and the overall clarity of the Fig.\n2.\nRevised Figure R5 a(Fig. 2h) Second derivative spectrum along the high-symmetry path M-K-Γ\nat 10.5 K (below T ). The dotted line enhances the visibility of the energy bands near the M point,\nCDW\nclearly revealing the band structure around VHS1 and VHS3. b(Fig. 2j) ARPES spectra from the\nmomentum-space trajectories. The yellow dashed line highlights the electron-like band, while the\ngreen dashed line indicates the hole-like band. The arrows in cut 3 indicate the appearance of VHS3.\n———— R E P L Y T O R E V I E W E R 3 ————\nReviewer #3 (Remarks to the Author):\n“I'm happy to see that the authors sincerely replied to all referees' concerns and,\nbased on that, thoroughly implemented revisions where appropriate.\nIn my view the revised version of the manuscript is thus suitable for publication in\nNature Communications.”\nResponse:\nWe sincerely thank the reviewer for the positive evaluation of our revised\nmanuscript and the constructive comments throughout the review process. The\ninsightful suggestions have been invaluable in strengthening our work.\n———— R E P L Y T O R E V I E W E R 1 ————\nReviewer #1 (Remarks to the Author):\n“The authors have addressed all referee comments appropriately, and I\nrecommend the manuscript for publication in Nature Communications.”\nResponse:\nWe sincerely thank the reviewer for their positive feedback and for recommending\nour manuscript for publication in Nature Communications."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I appreciate the authors’ efforts in addressing my comments and questions. A few more points require clarification before I recommend the manuscript for publication:\n1) The authors provided DFT calculated CEC (Extended Data Fig. 1) to illustrate the reported temperature depended Fermi surface reconstruction. However, I wonder how do these compare with the CEC at the Fermi level measured with ARPES. Is the Fermi surface reconstruction visible in the experimental data? If such data are available, one could potentially plot a differential CEC (CEC_130K - CEC_10K).\n2) Similarly to above, the authors could extract a differential E-k map, where they subtract the Extended Data Fig. 2e (10.5K) from Extended Data Fig. 2e (130K) (or those from Fig. 2e and 2g). This will highlight newly formed bands (VHS3) that emerge upon CDW phase transition.\nMinor tip: proper photoemission intensity normalization will be needed before the subtraction of the two spectra.\n3) Suggestion: My third comment is concerning the title of the manuscript. Maybe something like \"Photoresponse Enhancement upon Phase Transition-Induced Fermi Surface Reconstruction in Geometrically Frustrated Lattices\" would be more suitable, since the enhanced photoresponse is a key finding of the manuscript.", "reviewer_2": "The authors corrected the manuscript following the previous comments; now the logics look concrete.\nI just have a minor suggestion; the others seem to be fine to publish on Nature Communications.\n1) The colour of the capital 'VHS1' and 'VHS3' in Figure 2 (h) and (j) is hard to recognize. It would be better to change for the reader's convenience.", "reviewer_3": "I'm happy to see that the authors sincerely replied to all referees' concerns and, based on that, thoroughly implemented revisions where appropriate.\nIn my view the revised version of the manuscript is thus suitable for publication in Nature Communications."}, "author_response": "———— R E P L Y T O R E V I E W E R 1 ————\nReviewer #1 (Remarks to the Author):\n“I appreciate the authors’ efforts in addressing my comments and questions. A few\nmore points require clarification before I recommend the manuscript for publication:”\nResponse:\nWe are very grateful for the reviewer's overall positive assessment of our revisions\nand their continued engagement with our manuscript. We sincerely appreciate the\nopportunity to clarify the remaining points. Below we provide a point-by-point\nresponse to the additional comments.\nComment 1):\n“The authors provided DFT calculated CEC (Extended Data Fig. 1) to illustrate\nthe reported temperature depended Fermi surface reconstruction. However, I wonder\nhow do these compare with the CEC at the Fermi level measured with ARPES. Is the\nFermi surface reconstruction visible in the experimental data? If such data are\navailable, one could potentially plot a differential CEC (CEC 130K – CEC 10K).”\nResponse:\nWe sincerely thank the reviewer for raising this critical point and for proposing the\nhighly insightful differential CEC analysis. In response to reviewer’s suggestions, we\nconducted further analysis of the ARPES data. Our analytical findings are presented\nbelow:\nIn the original text, Fig. 2 displays high-resolution band dispersion measurements\nalong a high-symmetry direction at various temperatures. These results demonstrate\nclear band modifications when comparing the Pristine and ISD phases, with particular\nemphasis on the energy position of VHS3. This finding aligns with previous work (Phys.\nRev. Lett. 127, 236401). Our DFT calculation results clearly demonstrate the\nphenomenon of Fermi surface reconstruction. However, due to inherent limitations—\nsuch as the assumption in the calculations that the material is a perfect bulk at absolute\nzero—it is almost impossible for ARPES experimental results to completely reproduce\nthe DFT calculations. Furthermore,the ARPES analysis may be influenced by inherent\nexperimental limitations, such as, limited instrumental resolution, intrinsic thermal\nbroadening, and scattering from surface degradation.\nFollowing the reviewers' suggestions, we analyzed the CEC at the Fermi level (E\n= E ) for 130 K and 10.5 K (Fig. R1). Our experimental data exhibits subtle changes\nF\nbut the underlying electronic structure modification remains robust. Our experimental\nresults continue to support the core conclusion: the CDW phase transition induces\nsignificant band structure modifications.\nIn Fig. R2 a, the CEC measured at E= E −0.2 eV shows clear variations in spectral\nF\nintensity. Most notably, the density of states along the K–M–K (orange line segment)\ntrajectory is negligible at 130 K but becomes markedly enhanced at 10.5 K. This\ntemperature-dependent evolution is consistent with an electronic reconstruction driven\nby the CDW transition. We have included the Momentum Distribution Curve (MDC)\nalong the K−M−K direction in Figs. R2 a and b, where the spectral intensity at the\nVHS3 position is clearly enhanced at low temperatures. This strongly indicates that the\nband containing VHS3 shifts to lower energy at low temperatures, consistent with the\ncalculation results.\nFig. R3 presents thedifferential map of the E–k dispersion, revealing a pronounced\nintensity variation near the VHS3 feature. This observation confirms the downward\nenergy shift of the band hosting VHS3 at low temperatures. In Fig. R3c, the significant\ncolor difference within the boxed region indicates a clear energy shift of the electronic\nbands at different temperatures. In Fig. R4, we compare CECs at 10.5 K and 130 K\nacross multiple binding energies. Despite limitations in data quality, a discernible\ndifference induced by VHS3 is captured in the CEC at E= E −0.15 eV, as indicated by\nF\nthe yellow arrow. We thank the reviewer for this insightful suggestion, which has\nstrengthened our analysis.\nRevised Figure R1 Fermi surface (FS) mappings collected at 10.5 K (a) and 130 K (b).\nRevised Figure R2 constant energy contour plots at E= E −0.12 eV collected at 10.5 K (a) and\nF\nK and 130 K.\nRevised Figure R3(Supplementary Figure S4) ARPES spectra at 130 K (a) and 10.5 K (b) along\nthe M-K-Γ direction. c. The difference between spectra collected above and below T ; red (blue)\nCDW\ncorresponds to a negative (positive) difference.\nRevised Figure R4 Fermi surface and constant energy contour plots around the M point collected\nat 10.5 K (a) and 130 K (b). The constant energy contour plots at E= E −0.15 eV collected at 10.5\nF\nK (c) and 130 K (d).\nComment 2):\n“Similarly to above, the authors could extract a differential E-k map, where they\nsubtract the Extended Data Fig. 2e (10.5K) from Extended Data Fig. 2e (130K) (or\nthose from Fig. 2e and 2g). This will highlight newly formed bands (VHS3) that emerge\nupon CDW phase transition.\nMinor tip: proper photoemission intensity normalization will be needed before the\nsubtraction of the two spectra.”\nResponse:\nWe are grateful to the reviewer for this excellent suggestion. The differential E-k\nmap analysis is indeed a powerful method to visually highlight the subtle changes in\nthe electronic structure across the phase transition. We have performed this analysis as\nrecommended.\nFollowing the reviewer's suggestions, we subtracted the ARPES intensity map at\n10.5 K (T < T , Fig. 2g in the original manuscript) from that at 130 K (T > T ,\nCDW CDW\nFig. 2e). This differential map (E-k at 10.5K - E-k at 130K) is now presented as a new\nFigs. S4 c, d and e. Fig. R3e presents the differential map of the E–k dispersion,\nrevealing a pronounced intensity variation near the VHS3 feature. The significant color\ndifference within the boxed region indicates a clear energy shift of the electronic bands\nhosting VHS3 at different temperatures.\n“Fig. R3c and d display the difference in spectral intensity between data collected\nabove and below T , highlighting the redistribution of spectral weight. Red color\nCDW\ndenotes predominant low temperature features, while blue color is used for high\ntemperature. Fig. R3e presents the differential map of the E–k dispersion, revealing a\npronounced intensity variation near the VHS3 feature. The significant color difference\nwithin the boxed region indicates a clear energy shift of the electronic bands hosting\nVHS3 at different temperatures.” (SIPage 7, Lines 135-141)\nRevised Figure R3(Supplementary Figure S4) ARPES spectra at 130 K (a) and 10.5 K (b) along\nthe M-K-Γ direction. c. The difference between spectra collected above and below T ; red (blue)\nCDW\ncorresponds to a negative (positive) difference.\nComment 3):\n“Suggestion: My third comment is concerning the title of the manuscript. Maybe\nsomething like \"Photoresponse Enhancement upon Phase Transition-Induced Fermi\nSurface Reconstruction in Geometrically Frustrated Lattices\" would be more suitable,\nsince the enhanced photoresponse is a key finding of the manuscript.”\nResponse:\nWe sincerely thank the reviewer for this excellent and constructive suggestion\nregarding the manuscript title. We fully agree that the title should more prominently\nhighlight the key finding of our work—the substantial enhancement in photoresponse.\nThe proposed title, \"Photoresponse Enhancement upon Phase Transition-Induced\nFermi Surface Reconstruction in Geometrically Frustrated Lattices\", accurately\ncaptures the core narrative of our study.\nInspired by the reviewer's suggestion, we have refined the title to:\n“Harnessing Van Hove Singularities for Terahertz Photoresponse via Fermi\nSurface Reconstruction in Kagome Lattices”\n———— R E P L Y T O R E V I E W E R 2 ————\nReviewer #2 (Remarks to the Author):\n“The authors corrected the manuscript following the previous comments; now the\nlogics look concrete. I just have a minor suggestion; the others seem to be fine to publish\non Nature Communications.”\nResponse:\nWe would like to express our sincere gratitude for your time and valuable\ncomments on our manuscript. We are delighted to receive the positive feedback and\nhave carefully addressed the minor suggestion as detailed below. We believe the\nmanuscript has been further improved as a result.\nComment 1):\n“The colour of the capital 'VHS1' and 'VHS3' in Figure 2 (h) and (j) is hard to\nrecognize. It would be better to change for the reader's convenience.”\nResponse:\nWe sincerely thank the reviewer for pointing out the issue with the color contrast\nof the 'VHS1' and 'VHS3' labels in Figs 2h and 2j. We agree that improving the legibility\nof these labels is crucial for the reader's convenience and the overall clarity of the Fig.\n2.\nRevised Figure R5 a(Fig. 2h) Second derivative spectrum along the high-symmetry path M-K-Γ\nat 10.5 K (below T ). The dotted line enhances the visibility of the energy bands near the M point,\nCDW\nclearly revealing the band structure around VHS1 and VHS3. b(Fig. 2j) ARPES spectra from the\nmomentum-space trajectories. The yellow dashed line highlights the electron-like band, while the\ngreen dashed line indicates the hole-like band. The arrows in cut 3 indicate the appearance of VHS3.\n———— R E P L Y T O R E V I E W E R 3 ————\nReviewer #3 (Remarks to the Author):\n“I'm happy to see that the authors sincerely replied to all referees' concerns and,\nbased on that, thoroughly implemented revisions where appropriate.\nIn my view the revised version of the manuscript is thus suitable for publication in\nNature Communications.”\nResponse:\nWe sincerely thank the reviewer for the positive evaluation of our revised\nmanuscript and the constructive comments throughout the review process. The\ninsightful suggestions have been invaluable in strengthening our work."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have addressed all referee comments appropriately, and I recommend the manuscript for publication in Nature Communications."}, "author_response": "———— R E P L Y T O R E V I E W E R 1 ————\nReviewer #1 (Remarks to the Author):\n“The authors have addressed all referee comments appropriately, and I\nrecommend the manuscript for publication in Nature Communications.”\nResponse:\nWe sincerely thank the reviewer for their positive feedback and for recommending\nour manuscript for publication in Nature Communications."}]

Decision letter