Topologically enhanced giant broadband second-harmonic generation in Weyl semiconductor tellurium

Domain: physics
Published: 2025-11-24
Editorial outcome: accept

Abstract
Achieving strong nonlinear optical (NLO) responses in atomically thin layered materials is essential for advanced nanoscale photonic and on-chip integrated optoelectronic technologies. However, most materials with large second-order susceptibility (χ(2)) operate only over narrow wavelength ranges, with rare reports in the mid-infrared (MIR) region. Topological engineering provides a promising strategy to enhance NLO responses. Here, we demonstrate that Weyl semiconductor tellurium (Te) nanoflakes exhibit giant second harmonic generation (SHG) across an ultrabroadband infrared range (1.2-5.0 μm), including the challenging MIR region, achieving conversion efficiency two orders of magnitude greater than GaSe. The extracted χ(2) spectrum reveals a prominent peak of 5.0 ± 0.4 nm V-1 at 2.2-μm excitation and two shoulders, attributable to three two-photon resonances with interband transitions near three different Weyl cones, indicating topological enhancement of SHG. The giant, anisotropic, ultrabroadband SHG in Te nanoflakes promises unprecedented versatility for MIR frequency conversion and advanced MIR nonlinear optical devices.

Introduction
Second harmonic generation (SHG), a second-order nonlinear optical (NLO) process that refers to coherently combining two photons into one photon with twice of energy, occurs for crystals with broken inversion symmetry1. SHG plays a pivotal role in various applications, such as frequency conversion, coherent light generation, nonlinear auto and cross-correlations, optical signal processing and imaging2–4. For miniature optoelectronic and all-photonic device applications, particularly in on-chip integration, conventional NLO bulk crystals are usually not applicable due to their three-dimensional covalent bonding nature, large light-matter interaction volumes, and complex phase-matching requirements. In contrast, atomically thin layered materials, such as transition metal chalcogenides (TMDCs), offer a promising alternative owing to their bond-free integration capabilities, unique van der Waals interfaces, tunable nonlinearity and relaxed phase-matching conditions due to their atomic thickness5–8. However, it remains a challenge to achieve high nonlinear conversion efficiency with atomically thin layered materials due to limited light-matter interaction length, and a larger second-order NLO susceptibility (χ(2)) is urgently demanded to achieve high conversion efficiency for on-chip photonic circuits. Previous studies on SHG from atomically thin layered materials, such as MoS2 (refs. 9,10), WSe2 (refs. 6,11), PbSe (ref. 12), and NbIO2 (ref. 13), have demonstrated high SHG susceptibility, up to 190 pm V−1 at 1050 nm in NbIO2 benefiting from exciton resonance effects. However, these studies have been limited to the visible to near-infrared (NIR) wavelength region, and very limited solutions are available in the mid-infrared (MIR) region, a spectral range that is crucial for remote sensing, gas sensing, autonomous driving, night vision, and astronomy14,15. In addition, suitable atomically thin layered materials with larger χ(2) in MIR are highly desirable in realizing ultracompact integrated photonic and optoelectronic devices for various applications, such as MIR photodetection utilizing frequency up conversion16,17, MIR to telecom band light signal processing modules in free-space optical communications systems18, and MIR/NIR dual band supercontinuum light sources for sensing over optical coherence tomography in biomedicine19.

In parallel, it has been theoretically proposed and experimentally explored that various NLO responses can be enhanced by the Berry phase in topological materials, which promises a new technical route toward high-efficiency nonlinear conversion materials. Early theoretical work proposed that general NLO effects, including second-order responses, such as shift current and SHG, as well as third-order responses, such as the NLO Hall effect and Kerr rotations, can be described through topological quantities involving the Berry connection and Berry curvature using Floquet formalism20 and the response can possibly be enhanced by the Berry phase when the optical transition matches specific states that are topologically nontrivial. Experimentally, since 2019, the topological enhancement of the shift current response has already been demonstrated by photocurrent measurements on Weyl semimetals, such as TaAs (ref. 21) and TaIrTe4 (ref. 22), when the optical transitions are in the vicinity of the Weyl nodes. A similar attempt at SHG in the Weyl semimetal TaAs occurred even earlier, back to 2017, when experiments showed a large χ(2) of 7.2 nm V−1 at 1.5 eV (ref. 23). However, later, photon-energy-dependent measurements demonstrated a relatively large SHG response at 1.5 eV arising from the high-energy tail of the resonance at 0.7 eV, which ruled out the direct connection between the enhanced SHG response and low-energy Weyl Fermions24. Following these studies, SHG measurements of the newly established Weyl semiconductor tellurium (Te) in the NIR region (0.7–2.5 μm) have shown the best infrared performance among the reported atomically thin layered materials, with χ(2) reaching 5.58 nm V−1 at 2.3 μm, but experimentally, the measurement by Fu et al. is limited to NIR region or falls at the near infrared boundary of MIR wavelength range25. In terms of data interpretation, an inappropriate intraband model is used in Fu et al.’s work to describe the large SHG response to the topological nature of Te, which should be dominated by interband transitions in their measurement range. In addition, their numerical analysis has substantial discrepancy with previous calculations20,26,27. These deficiencies in experiment and interpretation undermined the claim regarding the correlation between the large SHG response and the numerically calculated Berry curvature dipole of Te. To date, the impact of the topological nature on the large SHG of topological materials remains elusive, especially for wavelengths further into the MIR region.

Even before the demonstration of large SHG in the NIR region, Te has received widespread attention because of its high carrier mobility, intriguing topological properties, excellent environmental stability and photoresponse in the MIR region28. The nanoflakes, belonging to the P321 or P3121 space group, maintain broken inversion symmetry regardless of thickness, in contrast to 2H-stacked TMDCs, which exhibit reversed inversion symmetry between odd and even layers. The band structure of Te nanoflakes reveals a topological electronic structure with multiple Weyl nodes, in agreement with angle-resolved photoemission spectroscopy (ARPES)29–32, magneto-transport33,34 and optical measurements35,36, establishing Te as a Weyl semiconductor. In addition, multiple experiments have already shown strong NLO effects of Te in the visible and NIR ranges25,37–39.

Here, we reinvestigate the SHG responses of Te nanoflakes with fundamental excitation wavelengths ranging from the NIR region (1.2 μm) to the MIR region (5.0 μm), revealing the intrinsically giant, highly anisotropic and ultrabroadband SHG response. The conversion efficiency of Te nanoflakes is two orders of magnitude greater than that of GaSe, a prominent atomical thin layered nonlinear NIR material40. The spectrum of extracted χ(2) shows three local maximums that match the major transitions at the vicinity of the three Weyl cones. Benefiting from the joint contribution from three different Weyl cones in conduction and valance band, Te exhibits a large topologically enhanced SHG response over a broad wavelength range covering both NIR and MIR, providing an ideal on-chip SHG crystal. Our numerical calculation of χ(2) shows consistency with experimental results when appropriate Fermi level and scattering rate at high excitation energies are incorporated. Overall, these findings not only directly provide a highly efficient SHG conversion materials in the MIR region, particularly in the context of on-chip integration, but also pave an alternative route for exploring stronger NLO responses through topological engineering of quantum matters.

Results
Basic characterization and anisotropic SHG responses
The Te nanoflakes used in our work were synthesized by a hydrothermal method and then transferred onto SiO2 (285 nm)/Si substrates through a drop-casting process (see Methods for synthesis details). Figure 1a displays the crystal structure of Te, where the one-dimensional (1D) helical atomic chains are arranged in a parallel assembly interconnected by van der Waals forces, stretching in the c-direction30. The crystallographic c-axis of the Te nanoflake can be identified from the long edge in the optical image and was further confirmed by polarization-dependent Raman spectroscopy. These basic characterizations of the Te nanoflake are presented in Supplementary Note 1.

To explore the second-order NLO properties of Te in the MIR region, we performed SHG measurements with excitation wavelengths ranging from 1.2 μm (1.03 eV) to 5.0 μm (0.25 eV), and the longest wavelength corresponds to the transition below the optical band gap of Te (~0.36 eV). All measurements were performed with the back-reflection geometry shown in Fig. 1b, and the polarization of the fundamental beam was set perpendicular to the crystallographic c-axis, unless otherwise specified. For SHG signals above 1.24 eV, a cooled silicon charge-coupled device (CCD) is used to detect the SHG signal; for SHG signals below 1.24 eV, a cooled single-cell InGaAs detector is used instead, with a detection efficiency much lower than that of the cooled silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from the difference frequency generation (DFG) system (~1.5 mW) with 250 kHz repetition rate and the notably lower efficiency of the InGaAs detector compared to a silicon CCD. Despite the limitations of the InGaAs detector, the SHG spectra still exhibit a good signal-to-noise ratio over the SHG spectrum range from 2.1 μm to 5.0 μm, as measured on an 18-nm Te nanoflake due to the giant SHG response Fig. 1c. The clear SHG signal implies that Te may possess a very large and broadband second-order NLO response in the MIR. Furthermore, a confocal scanning modality is used to obtain spatial mapping of the SHG intensities over an individual Te nanoflake Fig. 1d, e, further confirming the perfect single-crystalline quality and uniform thickness of the sample. Figure 1f shows the typical power-dependent SHG intensity under 4-μm excitation, which can be linearly fitted with a slope of 1.93, indicating the quadratic nature of the second-order NLO process. Figure 1g shows that the polarization direction of the SHG from Te nanoflakes is always linearly polarized along the a-axis regardless of the polarization of the fundamental excitation. In addition, the SHG intensity shows strong anisotropy with respect to the linear polarization direction of the fundamental beam, and only the linear polarization component along the crystallographic a-axis contributes to the SHG. These polarization characteristics of SHG with more thorough polarization-dependent measurements are consistent with the symmetry analysis of Te presented in Supplementary Note 2.

Giant broadband SHG responses
To compare the SHG conversion efficiencies, we conducted reference SHG measurements on exfoliated GaSe flakes and bulk TaAs in the same setup. GaSe is a well-known layered material with a large second-order NLO coefficient in the MIR region40–42, and TaAs is a bulk Weyl semimetal that exhibits large second-order NLO polarizability according to previous reports23. However, SHG signals from neither GaSe flakes nor TaAs in the MIR region (2.5 μm-5.0 μm) are detectable in our SHG measurement setup due to the limited excitation power of the fundamental light from

Methods

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors provided a very detailed answer to my previous report. The main issue I raised was around Fig. 4. The authors\nclarified both the comparison with existing calculations for the undoped Te in panel 4a and the phenomenological model\nused for comparison with the experiment in panels 4b,c accounting for the doping. In the current version of the manuscript\nthe authors present a new version of Figure 4, add explanations in the related text and some data on carrier relaxation time\nto the Supplemental Material. This addresses the main issue I raised and also my concerns about the contribution of this\nmanuscript with respect to the previous experimental+modelling study published on Te.\nI believe that the current version of the manuscript presents sufficient evidence to support their\ninterpretation of the SHG\nenhancement which is alternative to that presented previously. The results are thus noteworthy and deserve publication in\nNature Communication.", "reviewer_2": "This manuscript, originally considered by Nature Photonics, has been substantially revised. I previously supported its\nacceptance by Nature Photonics, with some technical comments. The authors have adequately addressed these comments\nin their revision, and I would have recommended acceptance by Nature Photonics.\nMost of the comments and authors’ responses focus on the relation of this work to Ref. 25. As I noted in my original review, I\ndo not believe the existence of Ref. 25 compromises the novelty of the present work. In the revised manuscript, the authors\nhave included detailed discussions on the significance of their new findings with respect to Ref. 25. This work not only\nsubstantially extends the experimentally accessed regimes, but also analyzes the data correctly. As such, it will help clarify\nsome of the confusion associated with Ref. 25.\nIn summary, I recommend acceptance of this manuscript by Nature Communications as is.", "reviewer_3": "The authors of the manuscript entitled “Topologically Enhanced Giant Broadband Second-Harmonic\nGeneration in Weyl Semiconductor Tellurium,” have made changes that, in my opinion, suitably address the issues raised by all reviewers and\nmake their manuscript suitable for publication in Nature Communications. However, I suggest that they address the following\npending (minor) issues before publication:\n1. In response to Reviewer 2, the authors amended their manuscript, which now states that, in Figure 1c, “The spectral\nbandwidth variation primarily arises from the filters used in the measurements”. I do not believe this is correct. The\ndifferences in SH bandwidth shown in the figure are more likely to be a consequence of the natural relationship between\npulse duration and spectral bandwidth, when the latter is shown in wavelengths (rather than frequency). For example, a\ntransform-limited 250-fs Gaussian pulse has a spectral width of 2 nm at 0.6 µm, of 8.5 nm at 1.2 µm, and of 34 nm at 2.4 µm.\nHowever, if the authors are correct and their filters are distorting the SH spectra, they must account for such a distortion in\ntheir chi(2) calculations.\n2. In the x axis of Figure 1f, the correct is “Peak excitation intensity” rather than “Peak excitation density”.\n3. The discussion in the paragraph extending between lines 271 and 313 (pages 9-11) of the main manuscript contains\ninaccuracies that make it rather confusing. First, the authors state that Fig. 4a compares experimental and calculated chi(2).\nHowever, the figure actually compares calculated chi(2) from 3 different papers (including the present paper). No\nexperimental data is shown. Second, there seems to be a confusion with the colors. The authors say that the curve\ncorresponding to their work is plotted in purple, and that the curve corresponding to Ref. 25 is plotted in red. To me, the\ncorrect used colors are blue and purple, respectively. Finally, still referring to Fig. 4a, the authors state that “However, both\ntheoretical results show significant deviation with the experiments. It's worth to note that our experimental results at high\nphoton energy from 1.0 to 2.1 eV are consistent with those in Fu et al’s work…” However, none of this can be concluded\nfrom the figure, as the latter does not contain any experimental data. The authors are encouraged to address all these\nissues.\n4. In lines 252-255 (page 13) of the Supporting Information, “… neglect phase mismatch owing to the reduced nanoflake\nthickness” would be correct than “… neglect phase matching owing to the reduced nanoflake thickness.” What I mean is: if\nthey do not include any phase matching calculations, they are assuming (rather than neglecting) phase matching."}, "author_response": "Response to the Reviewers\nWe sincerely thank all reviewers for their thoughtful feedback and constructive suggestions,\nespecially the firm support from reviewer 2. The suggestions from the reviewers have significantly\ncontributed to the improved clarity, quality, and presentation of our manuscript.\nReviewer #1 (Remarks to the Author):\nThe authors provided a very detailed answer to my previous report. The main issue I raised was\naround Fig. 4. The authors clarified both the comparison with existing calculations for the undoped\nTe in panel 4a and the phenomenological model used for comparison with the experiment in panels\n4b, c accounting for the doping. In the current version of the manuscript the authors present a new\nversion of Figure 4, add explanations in the related text and some data on carrier relaxation time\nto the Supplemental Material. This addresses the main issue I raised and also my concerns about the\ncontribution of this manuscript with respect to the previous experimental + modelling study published\non Te.\nI believe that the current version of the manuscript presents sufficient evidence to support their\ninterpretation of the SHG enhancement which is alternative to that presented previously. The results\nare thus noteworthy and deserve publication in Nature Communication.\nOur response: We are glad that our revisions can satisfy the high criteria of the reviewer, and are\ngrateful to the reviewer for final recommendation for its publication.\nReviewer #2 (Remarks to the Author):\nThis manuscript, originally considered by Nature Photonics, has been substantially revised. I\npreviously supported its acceptance by Nature Photonics, with some technical comments. The authors\nhave adequately addressed these comments in their revision, and I would have recommended\nacceptance by Nature Photonics.\nMost of the comments and authors’ responses focus on the relation of this work to Ref. 25. As I noted\nin my original review, I do not believe the existence of Ref. 25 compromises the novelty of the present\nwork. In the revised manuscript, the authors have included detailed discussions on the significance\nof their new findings with respect to Ref. 25. This work not only substantially extends the\nexperimentally accessed regimes, but also analyzes the data correctly. As such, it will help clarify\nsome of the confusion associated with Ref. 25.\nIn summary, I recommend acceptance of this manuscript by Nature Communications as is.\nOur response: We are very grateful for the reviewer’s appreciation of the significance of our work\nand firm support of reviewer 2.\nReviewer #3 (Remarks to the Author):\nGeneration in Weyl Semiconductor Tellurium,” have made changes that, in my opinion, suitably\naddress the issues raised by all reviewers and make their manuscript suitable for publication in\nNature Communications. However, I suggest that they address the following pending (minor) issues\nbefore publication:\nOur response: We thank the reviewer for the careful review. Below are point-by-point responses and\nthe corresponding changes that are made in the manuscript.\n1. In response to Reviewer 2, the authors amended their manuscript, which now states that, in Figure\n1c, “The spectral bandwidth variation primarily arises from the filters used in the measurements”. I\ndo not believe this is correct. The differences in SH bandwidth shown in the figure are more likely to\nbe a consequence of the natural relationship between pulse duration and spectral bandwidth, when\nthe latter is shown in wavelengths (rather than frequency). For example, a transform-limited 250-fs\nGaussian pulse has a spectral width of 2 nm at 0.6 µm, of 8.5 nm at 1.2 µm, and of 34 nm at 2.4 µm.\nHowever, if the authors are correct and their filters are distorting the SH spectra, they must account\nfor such a distortion in their chi(2) calculations.\nOur response: We thank the reviewer for highlighting this discrepancy on details. We agree with the\nreviewer that most differences in the SH bandwidths shown in Fig. 1c are primarily due to the\nvariation of the pulse duration and spectral bandwidth of the fundamental beam at different excitation\nwavelengths when tuning the output from our OPA and DFG. However, for certain measurements,\nspecifically at 1.2, 1.3, and 1.4 μm—we used bandpass filters with a 10–12 nm full width at half\nmaximum (FWHM) on the fundamental beam to precisely select the desired wavelength as stated\nin previous response. The application of filter on fundamental beam causes very large bandwidth\nvariation comparing with those wavelengths without applying a filter. The reason that we apply a\nfilter for 1.2-μm excitation is because 1.2 μm is at the short wavelength tuning limit of our OPA signal\nbeam and applying a filter help avoid the potential problems caused by distortion of the OPA signals.\nThe application of filter accounts for very narrow SHG spectrum at those specific wavelengths. Table\nR1 summarizes the bandpass filters used in the fundamental beam path for wavelength selection. Here,\nwe note, these bandpass filters were only applied to the fundamental beam, therefore, the bandpass\nfilter does not distort the SHG spectra.\nTable R1 | Bandpass filters used in the fundamental beam path.\nFundmental\nSHG Bandpass\nbeam\nCenter Center Center\nFWHM FWHM\nWavelength Wavelength Wavelength\n(nm) (nm)\n(nm) (nm) (nm)\n600 2.1 1200 1200 10\n650 3.4 1300 1300 12\n701 3.2 1402 1400 12\n2\n769 17.1 1538\n825 35.7 1650\n888 33.4 1776\n915 35.3 1830\n956 36.3 1911\n997 39.7 1993\n1055 40.2 2110\n1102 35.0 2204\n1150 65.1 2300\n1186 43.6 2372\n1251 29.3 2502\n1432 40.6 2864\n1470 54.0 2941\n1513 58.1 3026\n1562 61.5 3124\n1649 67.5 3298\n1725 65.4 3451\n1808 78.1 3617\n1935 88.7 3869\n2019 91.9 4039\n2285 80.1 4569\n2335 121.0 4669\n2430 98.8 4860\nTo avoid potential confusion and any misleading information about the application of bandpass\nfilters, we have updated Fig. 1c in the main text to use spectra obtained without bandpass filters at\n1.2–1.4 μm.\nTo provide a more accurate and rigorous description, we have revised the relevant section of the\nmanuscript.\n1) Original Fig. 1c of the main text:\n“…c, Normalized SHG spectra at different fundamental wavelengths ranging from 1.2 μm to 5.0\nμm. ”\n2) Since the center wavelength of the longest-wavelength SHG spectrum is 2495 nm, the\nexperimental fundamental wavelength range has been updated from 1.2–4.9 μm to 1.2–5.0 μm in\nall relevant sections of the revised manuscript.\nThese revisions are marked in red in the revised main text and Supporting Information.\n2. In the x axis of Figure 1f, the correct is “Peak excitation intensity” rather than “Peak excitation\ndensity”.\nOur response: We have changed the x-axis label in Fig. 1f to “Peak excitation intensity”:\n4\n“...f, A typical power dependence of SHG intensity under 4-μm excitation plotted on a logarithmic\nscale, a linear fit with a slope of 1.93 supports the quadratic dependence characteristic of the SHG…”\n3. The discussion in the paragraph extending between lines 271 and 313 (pages 9-11) of the main\nmanuscript contains inaccuracies that make it rather confusing. First, the authors state that Fig. 4a\ncompares experimental and calculated chi(2). However, the figure actually compares calculated chi(2)\nfrom 3 different papers (including the present paper). No experimental data is shown. Second, there\nseems to be a confusion with the colors. The authors say that the curve corresponding to their work\nis plotted in purple, and that the curve corresponding to Ref. 25 is plotted in red. To me, the correct\nused colors are blue and purple, respectively. Finally, still referring to Fig. 4a, the authors state that\n“However, both theoretical results show significant deviation with the experiments. It's worth to note\nthat our experimental results at high photon energy from 1.0 to 2.1 eV are consistent with those in Fu\net al.’s work…” However, none of this can be concluded from the figure, as the latter does not contain\nany experimental data. The authors are encouraged to address all these issues.\nOur response: We thank the reviewer for their careful reading and constructive feedback. We\napologize for the confusion and have addressed each point as follows:\nFirst, as the reviewer correctly noted, Fig. 4a in the original manuscript displayed only theoretically\ncalculated χ(2) values (our work, Ref. 25, and Ref. 26), with no experimental data shown. We have\nnow added our experimental data to Fig. 4a for a more comprehensive comparison.\nSecond, we have corrected the color assignments in both the figure and the main text for clarity: our\ntheoretical results are now shown in blue, while those from Ref. 25 are in purple.\nThird, with the experimental data now included in Fig. 4a, it’s easy to find that “both theoretical\nresults show significant deviation with the experiments”. In addition, we have clarified in lines 218–\n220 (page 8) of the main manuscript that our experimental data in the overlapping wavelength region\n(1.2–2.5 μm, corresponding to SH energies of 1.0 to 2.1 eV) are consistent with those of Fu et al.’s\nwork, and we have included the relevant citation.\nTo address and clarify all these issues, we have revised the manuscript as follows:\n1) We have revised the Fig. 4a and Fig. 4b in the revised manuscript:\n5\n“Fig. 4 | Numerical simulation of the SHG response of Te. a, Comparison of the experimentally\nextracted 𝜒(2) and theoretically calculated 𝜒(2) of undoped Te as a function of SH energy. The blue,\npurple, and gray curves correspond to the theoretical results from this work, ref. 25, and ref. 26,\nrespectively, while experimental points are illustrated with gray circles. b, Comparison of the\nexperimentally extracted 𝜒(2) and the theoretically calculated 𝜒(2) of Te at different Fermi levels…”\n2) In lines 271-274 (page 9) of the revised manuscript:\n“We first perform a theoretical calculation for intrinsic Te, which is shown as blue dashed curve in\nFig. 4a and successfully replicated the results by Guo's group (gray dashed curve)26, with minor\ndifferences likely stemming from variations in the χ(2) model and first-principle calculations.”\n3) In lines 278-280 (page 9) of the revised manuscript:\n“With regarding to the χ(2) calculations in Fu’s work25 (purple dashed curve in Fig. 4a), it becomes\nquite questionable due to the inconsistency with both Guo’s work26 and ours.”\n4) In lines 275-278 (page 9) of the revised manuscript:\n“It's worth to note that our experimental results at high photon energy from 1.0 to 2.1 eV are consistent\nwith those in Fu et al.’s work25 (as illustrated by the data in Fig. 2e), where the mechanism of SHG\nwere understood by a Berry curvature dipole (BCD)-dominated SHG model based on intraband\ntransitions…”\nThese revisions are marked in red in the revised main text and Supporting Information.\n4. In lines 252-255 (page 13) of the Supporting Information, “… neglect phase mismatch owing to\nthe reduced nanoflake thickness” would be correct than “… neglect phase matching owing to the\nreduced nanoflake thickness.” What I mean is: if they do not include any phase matching calculations,\nthey are assuming (rather than neglecting) phase matching.\nthe Supporting Information in lines 252-255 (page 13):\n“…and neglect phase matching mismatch owing to the reduced nanoflake thickness”\nOther changes:\n1. Author Affiliations:\nThe affiliations of the authors have been updated as follows:\nfrom\n“Delang Liang1,2, Mingyang Qin2, Yong Liu1, Weiming Wang3,4, Bin Cheng5, Xiao Zhuo2, Shiyu\nWang2, Zipu Fan2, Huawei Liu1, Guisen Chen1, Qinsheng Wang7, Changgan Zeng5, Anlian Pan1,5†,\nJinluo Cheng3,4†, and Dong Sun2,8,9† ”\nto\n“Delang Liang1,2, Mingyang Qin2, Yong Liu1, Weiming Wang3,4, Bin Cheng5, Xiao Zhuo2, Shiyu\nWang2, Zipu Fan2, Huawei Liu1, Guisen Chen1, Qinsheng Wang7, Changgan Zeng5, Anlian Pan1,5*,\nJinluo Cheng3,4,10*, and Dong Sun2,8,9,10*”\nA new affiliation has been added for Prof. Prof. Jinluo Cheng, due to a recent job transfer during the\nrevision process and Prof. Dong Sun now also holds a part-time position at the same institution:\n“10 School of Physics and Laboratory of Zhongyuan Light, Zhengzhou University, Zhengzhou,\nChina”\nIn addition, the symbol for corresponding authors has been changed from “†” to “*” to comply with\nthe formatting requirements of Nature Communications.\n2. Abstract:\nWe have reduced the length of the abstract from 213 to 150 words to comply with the formatting\nrequirements of Nature Communications:\n“Achieving strong nonlinear optical (NLO) responses in atomically thin layered materials is\nessential for advanced nanoscale photonic and on-chip integrated optoelectronic technologies.\nHowever, most materials with large second-order susceptibility (𝜒(2) ) operate only over narrow\nwavelength ranges, with rare reports in the mid-infrared (MIR) region. Topological engineering\nprovides a promising strategy to enhance NLO responses. Here, we demonstrate that Weyl\n7\nsemiconductor tellurium (Te) nanoflakes exhibit giant second harmonic generation (SHG) across an\nultrabroadband infrared range (1.2-5.0 µm), including the challenging MIR region, achieving\nconversion efficiency two orders of magnitude greater than GaSe. The extracted 𝜒(2) spectrum\nreveals a significant peak of 5.0 ± 0.4 nm V-1 at 2.2-μm excitation and two shoulders, attributable to\nthree two-photon resonances with interband transitions near three different Weyl cones, indicating\ntopological enhancement of SHG. The giant, anisotropic, ultrabroadband SHG in Te nanoflakes\npromises unprecedented versatility for MIR frequency conversion and advanced MIR nonlinear\noptical devices.”\n3. Fig. 3b of the main text manuscript:\nTo improve clarity and ensure consistency, we have exchanged the labels of the Weyl nodes W\n1\nand W in the updated Fig. 3b so that they correspond accurately to the shoulder features W and W\n3 1 3\nindicated in Fig. 3a. The main text has also been revised accordingly, with the changes marked in red\nin lines 248–254 (pages 9) and line 315-316 (page 11) of the revised manuscript.\n4. Languages:\nWe have made corrections to some grammatical and typographical errors in the manuscript to\nenhance its readability. For simplicity, we do not list them individually, but all corrections are marked\nin red in the revised manuscript."}]

Decision letter