Artificially structured materials have been broadly used to excite strong magnetic responses for the generation of crucial counterintuitive phenomena, including negative refraction, invisible cloaking, superlensing, etc.1,2. To overcome the weak magnetism of natural materials at optical frequencies, metallic molecules (e.g., split rings) with magnetic resonances induced by conduction current loops were proposed to construct artificial magnetic materials with negative refractive indices in the terahertz (THz) and mid-infrared ranges3,4. However, transferring magnetic resonances to higher frequencies (especially in the visible range) is restricted by the magnetic response saturation and stringent nanofabrication requirements5,6. Fortunately, magnetic resonances with the generation of displacement current loops were observed in specially designed plasmonic nanostructures, such as metallic nanopillar pairs6, tailored nanoclusters7, and particle-film systems8,9. These magnetic plasmon resonances (MPRs) possess excellent capabilities for engineering magnetism, confining light at the nanoscale, and enhancing the optical field in the high-frequency range, thus contributing to promising applications in light manipulation, perfect absorption, sensitive sensing and reinforced light-matter interactions6,7,8,9,10. To broaden the actual applications of MPRs, novel materials are currently highly desirable to open new doors for the generation and control of magnetic resonance behavior at optical frequencies. For example, graphene split rings were theoretically predicted to produce a magnetic resonant response stronger than traditional metallic structures, but their operating frequencies were limited to the far-infrared range11. Recently, topological insulators (TIs), as new quantum states of matter, have attracted wide attention in electronics, optics, and plasmonics12,13,14,15,16,17,18,19,20,21. TIs present unconventional conducting edge (or surface) states with topological protection caused by strong spin–orbit coupling of insulating bulk states, distinct from ordinary metals and insulators12,13. The time-reversal symmetry of edge (or surface) states with gapless Dirac fermions enables the avoidance of carrier backscattering from non-magnetic impurities13,14. The topological edge state was first confirmed in mercury telluride two-dimensional (2D) quantum wells12. Afterward, topological surface states with exotic Dirac cones were discovered in three-dimensional (3D) nanomaterials (e.g. Sb2Te3, Bi2Te3, and Bi2Se3)13,14. In 2019, thousands of materials were predicted to possess TI properties, paving a prospective path for quantum computing, spintronics, and devices with lower energy consumption22,23. Recently, Bi2Te3, Bi2Se3, and Bi1.5Sb0.5Te1.8Se1.2 TIs have been verified to display ultrahigh refractive indices and light-driven plasmonic activities in an ultrabroad optical range from ultraviolet (UV) to THz16,17,18,19,20,21. MPRs in TIs will be particularly useful for promoting the high-frequency optical activities of TIs and enriching their practical applications, especially in light-matter interactions. However, until now, MPRs and relevant applications have not been reported in TI systems.

Herein, we demonstrate for the first time, to our knowledge, a kind of visible range MPR effect in nanofabricated single-crystalline Sb2Te3 TI nanogrooves. The experimental results reveal that the MPR response has a particular dependence on the nanogroove height, width, and pitch, consistent with simulations and theoretical calculations. To explore actual applications of TI MPRs, we innovatively integrated monolayer MoS2 with a nanostructured TI to improve the intrinsically weak interactions between light and atomic-layer materials. Polarization-dependent photoluminescence (PL) emission was experimentally observed and reasonably analyzed. Benefitting from the strong MPR-induced electric field enhancement, the MoS2 PL intensity was remarkably reinforced compared with TI electric plasmon resonances (EPRs). These results will open a new door for exploring novel TI optical physics and applications in optoelectronic devices and artificial magnetic materials.


Optical constant and nanostructure of the Sb2Te3 single crystal

As shown in Fig. 1a, the TI nanogroove grating structure is fabricated on the surface of a Sb2Te3 single-crystal film using the focused ion beam (FIB) milling method (see “Materials and methods” section). The height, width, and pitch of the nanogrooves are denoted by h, d, and p, respectively. As a primary member of the 3D TI family, the Sb2Te3 material possesses distinctly discrepant surface and bulk states, exhibiting excellent optical characteristics13,15. Here, the Sb2Te3 single crystal is grown using the melting and slow-cooling method (see “Materials and methods” section). To clarify the material morphology, we employ transmission electron microscopy (TEM) to obtain the selected area electron diffraction (SAED) pattern and a high-resolution TEM (HRTEM) image of the Sb2Te3 microflake. The Sb2Te3 microflake depicted in Fig. 1b is fabricated through mechanical exfoliation and chemical etching methods (Supplementary Methods). As shown in Fig. 1c, the sharp diffraction spots and atomic lattice arrangement verify the hexagonal packed structure of the high-quality Sb2Te3 single crystal. The chemical composition is confirmed by energy-dispersive X-ray spectroscopy (EDS), revealing that the elemental molar ratio of Sb:Te is 2:3 (Supplementary Fig. S1). The high crystalline quality of Sb2Te3 can be further verified by the Raman spectrum (Supplementary Fig. S2). The complex relative permittivities of TI materials can be measured by a spectroscopic ellipsometer with considering the surface and bulk states17. The conducting surface and insulating bulk can be fitted with the Drude and Tauc–Lorentz dispersion formulas, respectively (Supplementary Methods). Figure 1d shows the fitted relative permittivity of single-crystalline Sb2Te3 in the UV, visible, and near-infrared ranges, which agrees well with the experimental results. The surface and bulk permittivities (εs and εb) are depicted in Fig. 1e, f, respectively. The surface permittivity satisfies the conditions of Re(εs) < 0 and −Re(εs) > Im(εs) at wavelengths from 250 to 2065 nm. This metal-like property of the surface state provides the possibility of generating the plasmonic response at high frequencies24,25,26. The negative permittivity of the bulk state at shorter wavelengths (from 253 to 760 nm) can be attributed to the strong interband electronic absorption similar to semiconductors17. Thus, the bulk state can also contribute to the formation of plasmonic resonances at visible wavelengths of less than 760 nm. The surface and bulk states together give rise to the negative permittivity of Sb2Te3 at wavelengths from 250 to 895 nm, as shown in Fig. 1d. The fitting results (Supplementary Table S1) illustrate that the Sb2Te3 bulk possesses a bandgap of ~0.33 eV, which is consistent with the reported 0.3 eV27. The Sb2Te3 surface presents an ultrathin layer of 2.6 nm (i.e., t = 2.6 nm), similar to the reported 2.5 nm for the TIs in the same family28. To the best of our knowledge, this is the first report of surface and bulk optical constants for the Sb2Te3 single crystal, laying the foundation for exploring Sb2Te3 optical activities and functionalities.

Fig. 1: TI nanostructure, material characterization, and optical constant.
figure 1

a Schematic of a Sb2Te3 TI nanogroove grating with height h, width d, and pitch p underneath monolayer MoS2. The light is incident on the nanostructure with a polarization angle of θ. b TEM high-angle annular dark-field (HAADF) image of a part of a thin Sb2Te3 microflake (inset) on the carbon support film of a copper microgrid. The dotted rectangle denotes the area selected for electron diffraction and high-resolution TEM. The right images are the EDS mapping pictures of the measured part of the Sb2Te3 microflake for determining the spatial distributions of elements Sb and Te. c SAED pattern and HRTEM image (inset) of the Sb2Te3 single crystal. d Measured (circles) and fitted (curves) relative permittivities of the Sb2Te3 single crystal in the UV, visible, and near-infrared ranges. The fitted real and imaginary permittivities are obtained from the ellipsometer software with a layer-on-bulk model (inset) for the Sb2Te3 TI. e, f Real and imaginary permittivities of the conducting surface and insulating bulk.

Magnetic plasmon resonances in Sb2Te3 nanostructures

First, a nanogroove grating with h = 110 nm, d = 130 nm, and p = 450 nm is fabricated on the Sb2Te3 film (with a thickness of >300 nm) mechanically exfoliated onto a Si substrate. Scanning electron microscopy (SEM) and atomic force microscopy (AFM) are used to measure the structural profile of the nanogrooves, as shown in Fig. 2a, b, respectively. The reflection spectra from the Sb2Te3 nanogroove grating are measured using a micro-spectrometer system (see “Materials and methods” section). The experimental results in Fig. 2c reveal that the incident light with polarization perpendicular to the nanogrooves (i.e., θ = 0°) possesses a distinct reflection dip at ~736 nm. However, the reflection dip disappears when the polarization is parallel to the nanogrooves (i.e., θ = 90°). The finite-difference time-domain (FDTD) numerical simulations (see “Materials and methods” section) agree well with the experimental results, as depicted in Fig. 2d. To clarify the reflection mechanism, we plot the magnetic and electric field distributions at the reflection dip when θ = 0°, as shown in Fig. 2e, f, respectively. Interestingly, the magnetic field energies are enhanced and are mainly concentrated in the Sb2Te3 nanogrooves, exhibiting a strong diamagnetic effect. In Fig. 2f, the arrows indicate the direction and amplitude of the electric field vector, revealing the generation of displacement current loops in the nanogrooves. The electric current along the nanogroove surface is excited by the magnetic field component parallel to the Sb2Te3 nanogroove (Supplementary Fig. S3). The visible range resonance generated in this split-ring-like TI nanostructure is regarded as a typical magnetic resonance similar to MPR29. When the magnetic field component of incident light is perpendicular to the nanogrooves (i.e., θ = 90°), the magnetic resonance cannot be effectively excited, restraining the appearance of the reflection dip. Under the resonant condition, the TI surface charges accumulate at the upper corners of the nanogrooves, accompanied by a strong electric field intensity (|E/Ei|2) enhancement of >200-fold, as depicted in Fig. 2f. From Fig. 2c, we find that TIs can present a broader MPR (or MPR-like) spectrum than metals. The broad MPR spectrum contributes to a relatively large wavelength range for strong field enhancement. The significant field enhancement in nanostructured TIs will open a new door for the improvement of nanoscale light-matter interactions. It is worth noting that the TI surface layer contributes to the redshift and narrowing of the resonant spectrum17 (Supplementary Fig. S4a). At the MPR wavelength, the TI surface and bulk present absorption peak values of ~6% and ~94%, respectively (Supplementary Fig. S4b).

Fig. 2: Structure characterization, reflection spectra, and MPR field distribution of TI nanogrooves.
figure 2

a Top-view SEM image of the Sb2Te3 nanogroove grating with h = 110 nm, d = 130 nm, and p = 450 nm. The scale bar is 2 μm. The inset shows an SEM image of Sb2Te3 nanogrooves with a 52-degree view. b Corresponding AFM image of the Sb2Te3 nanogrooves and the nanogroove height profile along the white line. c, d Experimentally measured and numerically simulated reflection spectra from the Sb2Te3 nanogroove grating when θ = 0° and 90°. e Distribution of the magnetic field |H/Hi| in a periodic unit of Sb2Te3 nanogrooves at the MPR wavelength when θ = 0°. f Corresponding distribution of electric field |E/Ei|. The arrows indicate the directions and relative magnitudes of the electric field. Here, Hi and Ei are the magnetic and electric field amplitudes of the incident light, respectively.

Subsequently, we investigate the dependence of the magnetic resonance on the structural parameters (i.e., height h, width d, and pitch p) of the Sb2Te3 TI nanogrooves. Figure 3a shows that the reflection dip presents a distinct redshift with increasing h when θ = 0°. The MPR wavelength has a nearly linear relationship with h when p = 450 nm and d = 130 nm, as depicted in Fig. 3b. The experimental results are in excellent agreement with the numerical simulations. The MPRs can be reasonably analyzed by a mutual inductor–inductor–capacitor (MLC) circuit model30. The MPR wavelength can be described as λM = 2πc[(L + M)C]0.5, where L, M, and C are the inductance containing the nanogroove ridge inductance/kinetic inductance, the mutual inductance between two adjacent circuits, and the capacitance between two nanogroove ridges (Supplementary Methods). According to the MLC circuit model, we can theoretically deduce the MPR wavelength in the Sb2Te3 nanogrooves. The theoretical calculations are well consistent with the experimental and simulation results, as shown in Fig. 3b. The MLC circuit model indicates that the MPR response is also dependent on the nanogroove width d. Here, we measure the reflection spectra from the Sb2Te3 nanogroove gratings with different d when h = 110 nm and p = 450 nm. The experimental results in Fig. 3c demonstrate that the MPR wavelength exhibits a blueshift as d increases, which agrees well with the simulations (Supplementary Fig. S5). We also find that the MPR response also depends on the pitch of the nanogroove grating. The experiments in Fig. 3d show that the MPR wavelength redshifts with increasing p, in accordance with the simulations (Supplementary Fig. S5). From the MLC circuit model, we can see that the mutual inductance M increases with p, giving rise to the redshift of λM. The nanogroove height, width, and pitch are the effective parameters for the tuning and selection of MPR wavelengths in TIs.

Fig. 3: Measured MPR spectral response of TI nanogrooves with different structural parameters.
figure 3

a Experimentally measured reflection spectra from the Sb2Te3 nanogroove grating with different heights h = 100, 110, 120, 130, and 140 nm when d = 130 nm, p = 450 nm, and θ = 0°. b Corresponding MPR wavelengths of Sb2Te3 nanogrooves with different h. The experimental, simulation, and theoretical results are obtained by the micro-spectrometer, FDTD method, and MLC circuit model, respectively. c, d Experimentally measured reflection spectra from the Sb2Te3 nanogroove grating with different widths d = 130, 170, and 210 nm, when h = 110 nm, p = 450 nm, and θ = 0° and with different pitches p = 400, 450, and 500 nm, when h = 120 nm, d = 170 nm, and θ = 0°.

PL emission from the monolayer MoS2/Sb2Te3 nanogroove heterostructure

As mentioned above, the magnetic resonance in the TI nanostructure with strong field enhancement may offer a promising route for boosting light-matter interactions. Transition metal dichalcogenides (TMDCs), as a kind of 2D materials with unique semiconductor-like band structures, are regarded as a favorable platform for advancing next-generation optoelectronics due to the unique electric, mechanical and optical properties31,32. As a prototypical TMDC semiconductor, MoS2 possesses a state transition from an indirect bandgap of 1.2 eV to a direct bandgap of 1.8 eV as it transforms from bulk to monolayer31,33. The photoemission, excitonic binding, and chemical stability of monolayer MoS2 have drawn wide attention for the PL emission, promoting the achievement of atomically thin active light emitters and sources33,34,35. However, the atomically thin layer with poor light-matter interactions hinders the substantial application of MoS2 for light harvesting and emission33,35. Here, we innovatively integrate a MoS2 atomic monolayer with a Sb2Te3 TI nanostructure to explore the tailoring and enhancement of PL emission. As depicted in Figs. 1a and 4a, a MoS2 flake is mechanically exfoliated and coated on the Sb2Te3 nanogrooves using the fixed-point transfer method (see “Materials and methods” section). Figure 4b, c shows SEM images of the Sb2Te3 nanostructure before and after transferring the MoS2 flake, respectively. We can see that the MoS2 layer is precisely transferred onto the Sb2Te3 film with fabricated nanogrooves. The nanogroove grating is fabricated with h = 50 nm, d = 130 nm, and p = 400 nm on the Sb2Te3 film with a thickness of ~200 nm, as shown in Fig. 4d, e. The Raman spectrum in Fig. 4f shows that the in-plane vibrational mode \(E^1_{2g}\) and out-of-plane vibrational mode A1g can be excited when a 532 nm laser beam impinges onto the MoS2 layer over Sb2Te3. The frequency difference between the \(E^1_{2g}\) and A1g modes is ~18.5 cm1, which agrees well with the reported value of monolayer MoS234. As depicted in the inset of Fig. 5a, the Sb2Te3 nanogroove grating with monolayer MoS2 presents a reflection dip at ~532 nm when θ = 0° while retaining a high reflection when θ = 90°. This illustrates that the magnetic resonance can be generated at ~532 nm in the monolayer MoS2/Sb2Te3 nanogroove heterostructure. The numerical simulations are consistent with the experimental results (Supplementary Fig. S6). To reveal the light–MoS2 interaction enhancement, we demonstrate the luminescence emission response in the monolayer MoS2/Sb2Te3 nanogroove heterostructure using a confocal micro-spectrometry system with an excitation wavelength of 532 nm. Figure 5a displays the PL intensity spectra of the heterostructure for different incident polarization angles. Two PL peaks occur at 674.5 and 618.0 nm when θ = 90°, as can be more clearly seen in Supplementary Fig. S7. The inset of Fig. 5b depicts the PL intensity map spectrally integrated from 665 to 695 nm in the dashed square frame of Fig. 4a when θ = 0°. We can see that the Sb2Te3 nanogrooves with MoS2 can effectively excite the PL signal, while the Sb2Te3 nanogrooves cannot solely emit upon photoexcitation, as shown in Fig. 5c. The above two PL peaks correspond to the positions of the A and B direct excitonic transitions for monolayer MoS2 at the K point of the Brillouin zone36. The two resonances derive from the energy splitting from spin–orbit coupling of the valence band in monolayer MoS236,37,38. The MoS2 PL emission is sensitive to the substrate. The PL emission intensity of MoS2 on SiO2 will be stronger than that of MoS2 on the TI film. As shown in Fig. 5a, the intensities of the PL peaks drastically increase with the decrease in θ from 90° to 0°. The PL emission intensity with θ = 0° is particularly enhanced compared with the case of θ = 90°. Actually, the PL emission improvement is mainly dependent on the electric field enhancement in luminescent materials21,31,37. To clarify the mechanism of PL reinforcement, we numerically calculate the integrated electric field intensity in the Sb2Te3 nanogrooves. In contrast with the electric field with θ = 90°, we find that the enhancement factor of the integrated electric field intensity at 532 nm monotonically decreases as θ increases from 0° to 90°. As shown in Fig. 5b, the enhancement factor of the electric field intensity is close to the reinforced strength of the MoS2 PL excitonic peak. Therefore, the electric field enhancement plays a critical role in the PL reinforcement. In addition, the MoS2 PL emission is influenced by the support structures. The low reflection at the exciton wavelength may weaken the detected PL emission (Supplementary Fig. S8). Moreover, the PL peak wavelengths exhibit a linear redshift with decreasing θ, as depicted in Fig. 5d. The shifts satisfy the relations λ = 679.108–0.064θ and λ = 636.518–0.223θ for the two PL peaks. When θ = 0°, the PL peaks can approach the 680.5 and 638.0 nm wavelengths. Here, the redshift of the PL peak can be attributed to the generation of trions (a type of quasi-particle state) in monolayer MoS2 induced by the doping of MPR-excited hot electrons37,38. The A− trion, neutral A exciton, and B exciton in MoS2 can be extracted by fitting the PL spectrum using the multi-Lorentzian fitting method38. The MoS2 A− trion, A exciton, and B exciton peaks approximately localize at 687.4, 673.2, and 618.0 nm (i.e., 1.80, 1.84, and 2.01 eV) in the heterostructure with θ = 90°, respectively (Supplementary Fig. S7). The A exciton dominates the MoS2 PL emission when θ = 90° and decays with decreasing θ, while the A− trion increases gradually. This may stem from the higher hot-electron doping in MoS2 induced by the stronger magnetic resonance in the nanogrooves with smaller θ38. This phenomenon confirms the exciton-trion competition in plasmon systems37. The MPR-induced field enhancement and exciton-trion competition result in the different portions of the A exciton and A-trion/B exciton when θ changes from 90° to 0° (Supplementary Fig. S7). The appearance of hot electron-induced trions may also cause the reduction of the PL enhancement37. The energy shift of the A peak is 20 meV when θ changes from 90° to 0°, identical to the binding energy of trions in monolayer MoS238. The dependence of the PL emission height and position on the incident polarization offers a controllable scheme for tailoring light–MoS2 interactions in artificial nanostructures. As depicted in Fig. 5c, the PL emission of monolayer MoS2 based on MPR shows a strong reinforcement of 21-fold, a remarkable value compared with that of EPRs on TI nanoplates21. It should be noted that the PL emission reinforcement mainly results from the enhancement of the integrated electric field intensity in the laser impingement area. Therefore, the reinforcement of the PL intensity is lower than that of the electric field in Fig. 2f. As shown in Fig. 4f, the Raman signal can be improved by one order of magnitude with the generation of magnetic resonance.

Fig. 4: Structure and material characterization of the monolayer MoS2/Sb2Te3 nanogroove heterostructure.
figure 4

a Optical microscope image of Sb2Te3 nanogrooves with a transferred MoS2 layer. The area marked by the cyan dashed line denotes the MoS2 layer. The area on the right side of the dashed-dotted line represents monolayer (1 L) MoS2. The scale bar is 2 μm. b, c SEM images of Sb2Te3 nanogrooves before and after transferring MoS2. The scale bar is 2 μm in b. d AFM image of Sb2Te3 nanogrooves with MoS2. e AFM-measured height profiles of the Sb2Te3 film and nanogrooves at the positions along the red and blue lines in d. f Raman spectra of the MoS2 layer on the Sb2Te3 TI film and nanogrooves excited with the 532 nm laser when θ = 0°.

Fig. 5: PL emission response of the monolayer MoS2/Sb2Te3 nanogroove heterostructure.
figure 5

a PL emission spectra of the monolayer MoS2/Sb2Te3 nanogroove heterostructure for different incident polarization angles θ. The inset shows the reflection spectra of Sb2Te3 nanogrooves with monolayer MoS2 when θ = 0° and 90°. b Enhancement factors of the integrated electric field intensity in Sb2Te3 nanogrooves at 532 nm and PL emission at the A excitonic peak of monolayer MoS2 for different θ compared to the case of θ = 90°. The inset shows the PL intensity map spectrally integrated in the range of 665–695 nm when θ = 0° in the nanogroove area marked as the white dashed square frame in Fig. 4a. The scale bar is 1 μm. c PL emission spectra from the Sb2Te3 nanogrooves and monolayer MoS2 on the Sb2Te3 film/nanogrooves. d Dependence of A and B excitonic peak wavelengths on θ.


In this article, the topological optical features of a Sb2Te3 single crystal have been experimentally demonstrated. The results show that the surface and bulk states of the Sb2Te3 TI exhibit obvious metal- and semiconductor-like characteristics in the range from UV to near-infrared, respectively, enabling plasmonic excitation at high frequencies. Visible range MPR-like magnetic resonances were first observed in Sb2Te3 nanogrooves nanofabricated using the FIB milling method, breaking through the research limitation of TI EPRs16,17,18,19,20,21. Both the experimental and simulation results indicate that this MPR response particularly depends on the structural parameters. More specifically, the MPR wavelength redshifts with increasing nanogroove height and pitch, while it presents a blueshift with increasing nanogroove width. The MPR behavior can be effectively analyzed by the MLC circuit theoretical model. To explore potential applications of this MPR effect, we have integrated an advanced 2D nanomaterial (i.e., monolayer MoS2) with TI nanostructures to boost the light-matter interactions as an example. The experimental results show that the PL emission of monolayer MoS2 can be dramatically reinforced with MPR generation, breaking the intrinsic limitation of the poor interaction between light and atomically thin materials. The peak intensities and wavelengths of the MoS2 PL can be tuned by adjusting the polarization angle of the incident light, which can be attributed to the resonance-induced polarization-dependent electric field enhancement and generation of the A− trion. The MoS2 PL emission can be reinforced by 21-fold based on the MPRs in TI nanostructures, remarkably compared with TI-based EPRs21. The conventional Au material can also effectively promote the PL emission of MoS239. TIs can support plasmons at wavelengths from UV to THz16,17,18,19,20,21, making the generation of electric/magnetic resonances in an ultrabroad range possible. The excited wavelengths for Au-based PL enhancement can be extended by TI-based plasmons. The resonant field enhancement in the TI nanogrooves may not be the highest value, but the resonance spectral width with strong field enhancement is particularly broad. When the resonance wavelength is located around the MoS2 PL peak position, the electric field at 532 nm can still be enhanced by >100 times, which results in obvious MoS2 PL reinforcement (Supplementary Fig. S9). We find that the field enhancement can be further promoted through structural modification (Supplementary Fig. S10), enabling more applications of TIs in optical devices, such as nanoscale light sources, nonlinear frequency converters, and light-harvesting elements. This kind of magnetic resonance can also be generated in other TIs, such as Bi2Te3 and Bi2Se3. The various structures, such as nanopillars6, nanoclusters7, nanoparticles on film8,9, and nanocups10, will further enrich MPR effects in TI systems. These results not only enrich TI optical physics but also advance applications of TIs in optoelectronic devices and artificial magnetic materials.

Materials and methods

Growth of the Sb2Te3 single crystal

The high-quality Sb2Te3 single crystal is grown using the melting and slow-cooling method. High-purity Sb and Te powders with an atomic ratio of 2:3, as the starting materials, are sealed in a quartz tube. The crystals can be grown in a vertical furnace according to the following procedures: (1) The Sb and Te mixed powders are heated to 900 °C and completely melt. (2) The temperature is reduced quickly to 650 °C at a rate of 60 °C/h and then slowly to 550 °C at a rate of 2 °C/h. (3) The mixture is naturally cooled to room temperature. The Sb2Te3 single-crystalline character and stoichiometry can be confirmed by TEM, Raman, and EDS characterization.

Fabrication of Sb2Te3 nanostructures and transfer of MoS2

The Sb2Te3 film is mechanically exfoliated on a Si substrate using “Scotch” tape from the Sb2Te3 single crystal. The nanogroove grating is fabricated on the Sb2Te3 film using a FIB milling system (FEI Helios G4 CX) with a 30 kV voltage and a 7.7 pA current. The beam current should be controlled at a relatively low level for robust FIB fabrication. The MoS2 flakes are fabricated by exfoliating them from the MoS2 bulk material, repeatedly peeling them off with tape, and sticking them on a polydimethylsiloxane (PDMS) film. If a MoS2 flake on the PDMS has the most transparent area of several microns in size, then the MoS2 flake is transferred onto the Sb2Te3 nanogrooves using an optical microscope/micromanipulation system. Thus, the dry fixed-point transfer of MoS2 is completed.

Characterization of materials and nanostructures

The electron diffraction pattern and high-resolution TEM image of the Sb2Te3 single crystal are obtained by TEM equipment (FEI Talos F200X) with a voltage of 200 kV. Raman spectra of MoS2 and Sb2Te3, as well as PL emission spectra, are acquired using confocal micro-spectrometry (WITec Alpha 300R) with a linearly polarized 532 nm laser and an adjustable beam size (minimum diameter: 400 nm). SEM images of Sb2Te3 nanostructures are acquired by SEM equipment integrated with the FIB (FEI Helios G4 CX) using a 5 kV voltage and a 21 pA current. To avoid damaging the TI material, the beam current should not be too high (<43 pA) for SEM imaging. AFM images and height profiles of Sb2Te3 nanostructures are obtained by a commercial AFM system (Bruker). The relative permittivity of the Sb2Te3 single crystal in the UV, visible and near-infrared ranges is measured by a spectroscopic ellipsometer (HORIBA) with an angle of 70° for incident light. Reflection spectra from Sb2Te3 nanogrooves with/without MoS2 are measured by a home-made micro-spectrometer with a white light source impinging on the sample through a microscope and then reflected onto a CCD camera with a spectrometer (Andor).

Numerical simulations

The reflection spectra and field distributions of Sb2Te3 nanostructures are numerically simulated using the FDTD method20,40,41. The perfectly matched layer absorbing boundary condition and periodic boundary condition are set at the top/bottom and left/right sides of the computational space, respectively. A non-uniform mesh is employed in the x and z axis directions of TI nanostructures. The maximum mesh steps of the Sb2Te3 surface layers and monolayer MoS2 (0.615 nm) are set as 0.3 nm and 0.1 nm, respectively. The maximum mesh step of the Sb2Te3 bulk layer, air, and Si substrate is set as 5 nm. The relative permittivities in Fig. 1e, f are set for the surface and bulk states of the Sb2Te3 TI, respectively. The complex relative permittivity of the Si substrate is achieved from experimental data42. The relative permittivity of monolayer MoS2 measured by Li et al. is used in the simulations43. The reflection spectra are calculated using R = |Pr/Pi|, where Pi and Pr are the light powers incident on and reflected from the Sb2Te3 nanostructures, respectively.