Quantum-sized topological insulators/semimetals enable ultrahigh and broadband saturable absorption

Abstract

Two-dimensional topological insulators/semimetals have recently attracted much attention. However, quantum-sized topological insulators/semimetals with intrinsic characteristics have never been reported before. Herein, we report the high-yield production of topological insulator (i.e., Bi₂Se₃ and Sb₂Te₃) and semimetal (i.e., TiS₂) quantum sheets (QSs) with monolayer structures and sub-4 nm lateral sizes. Both linear and nonlinear optical performances of the QSs are investigated. The QS dispersions present remarkable photoluminescence with excitation wavelength-, concentration-, and solvent-dependence. The solution-processed QSs-poly(methyl methacrylate) (PMMA) hybrid thin films demonstrate exceptional nonlinear saturation absorption (NSA). Particularly, Bi₂Se₃ QSs-PMMA enables record-high NSA performance with a broadband feature. Specifically, the (absolute) modulation depths up to 71.6 and 72.4% and saturation intensities down to 1.52 and 0.49 MW cm⁻² are achieved at 532 and 800 nm, respectively. Such a phenomenal NSA performance would greatly facilitate their applications in mode-locked lasers and related fields.

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New concepts

Topological insulators and semimetals are important classes of 2D materials. Their quantum sheets (QSs) can be treated as extremely quantum-sized topological insulators/semimetals, whose production is highly desired but is far from satisfactory. We herein report the high-yield (>12 wt%) production of topological insulator (i.e., Bi₂Se₃ and Sb₂Te₃) and semimetal (i.e., TiS₂) QSs with monolayer structures and sub-4 nm lateral sizes. The QSs-poly(methyl methacrylate) (PMMA) hybrid thin films demonstrate exceptional nonlinear saturation absorption (NSA). Ultrahigh nonlinear response (72.4 and 68.4%) and ultralow power excitation (0.49 and 0.80 MW cm⁻²) are simultaneously achieved in both Bi₂Se₃ QSs-PMMA and TiS₂ QSs-PMMA. Such phenomenal NSA performances in quantum-sized topological insulators/semimetals would greatly facilitate their applications in mode-locked lasers and related fields.

1. Introduction

Two-dimensional (2D) materials have attracted much interest over the past decade due to their fascinating structures and properties.^1,2 Topological insulators (e.g., Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃) and semimetals (e.g., TiS₂ and TiSe₂) are important classes of 2D materials, which have emerged as the new frontiers of materials science.^3,4 Both topological insulators and semimetals possess extraordinary properties. The former features a gapless metallic state on their surfaces/edges and insulator characteristics in the bulk,⁵ while the latter is characterized by bulk Dirac or Weyl fermions and nontrivial topological surface/edge states.⁶ Such unique materials have been widely applied in various fields such as quantum physics,⁷ spintronics and magnetoelectronics.^3,6 Compared with bulk layered materials and conventional 2D materials, extremely quantum-sized 2D materials (e.g., 2D quantum sheets (QSs)) demonstrate remarkable performances because of their (both in-plane and out-of-plane) quantum confinement and prominent edge effects.⁸ The production of 2D QSs of topological insulators and semimetals is highly desired but far from satisfactory. Fortunately, we have recently developed a general strategy towards the production of 2D QSs and zero-dimensional quantum dots (0D QDs) from their bulk materials.^8–13 However, whether the strategy could be applied for topological insulator and semimetal QS production has never been testified.

Nonlinear optical (NLO) response is the key factor for the evaluation of NLO materials. As a typical third-order NLO effect, nonlinear saturation absorption (NSA) has attracted growing attention due to their applications in mode-locked lasers and related fields.¹⁴ 2D materials have shown their great potential in NSA by having a deep modulation depth and low saturation intensity.¹⁵ Recently, quantum-sized materials have demonstrated exciting NSA performances.^8–13 Meanwhile, topological insulators and semimetals are interesting candidates for NSA thanks to their unique electronic structures.^16,17 Therefore, quantum-sized topological insulators and semimetals could be very promising in terms of NSA performances.

Herein, we report the successful production of topological insulator (i.e., Bi₂Se₃ and Sb₂Te₃) and semimetal (i.e., TiS₂) QSs directly from their bulk materials using an all-physical top-down method. The combination of silica-assisted ball-milling and sonication-assisted solvent exfoliation enabled the high-yield (>12 wt%) production of QSs with monolayer structures and extremely reduced lateral sizes (<4 nm). The as-produced QSs were structurally intrinsic, which could be determinative to their unique photoluminescence (PL) and NSA performances. The QS dispersions presented excitation wavelength-, concentration-, and solvent-dependent PL. The QSs-poly(methyl methacrylate) (PMMA) hybrid thin films demonstrated exceptional NSA performances. Particularly, the Bi₂Se₃ QSs-PMMA realized ultrahigh nonlinear response and ultralow power excitation at wavelengths of 532 and 800 nm.

2. Results and discussion

The production process of Bi₂Se₃ QSs is schematically illustrated in Fig. 1(a), where four sequential procedures: silica-assisted ball-milling, sonication-assisted solvent exfoliation, centrifugation and filtration were involved.⁸ Sb₂Te₃ QSs and TiS₂ QSs were produced by the same method.⁸ Excitingly, a single cycle of the production process enabled production of Bi₂Se₃ QSs, Sb₂Te₃ QSs, and TiS₂ QSs from their bulk materials (>50 μm, Fig. S1a–c, ESI†) with extremely high yield of 14.6, 12.1, 15.8 wt%, respectively, suggesting their great potential for future industrialization. No precipitation was observed for the QS redispersions (2 mg mL⁻¹) when standing still for 7 days under ambient conditions, indicating their long-term stability. Zeta potentials were measured to be −22.5, −27.6, −33.6 mV for Bi₂Se₃ QS, Sb₂Te₃ QS, and TiS₂ QS aqueous redispersions (0.1 mg mL⁻¹), respectively (Fig. S4, ESI†), supporting their satisfactory stability.

Fig. 1 Scalable production and microscopic characterization of the Bi₂Se₃ QSs. (a) Schematic illustration of the fabrication process. (b) Schematic diagram of the crystal structure. (c) TEM image. (d) Corresponding lateral size distribution. (e) AFM image. (f) Corresponding height distribution. (g) HRTEM image (inset showing the corresponding FFT pattern). (h) XRD patterns. Data for bulk Bi₂Se₃ are shown for comparison. (i) High-magnification AFM image (inset showing the corresponding height profile).

The crystal structure of the Bi₂Se₃ is schematically illustrated in Fig. 1(b), where the monolayer was constituted by five atomic layers. Multiple microscopic techniques were utilized for characterization of the Bi₂Se₃ QSs. Fig. 1 shows the corresponding transmission electron microscopy (TEM) and atomic force microscopy (AFM) images. The microscopic characterization of the Sb₂Te₃ QSs and TiS₂ QSs can be found in Fig. S2 and S3 (ESI†). From Fig. 1(c), the Bi₂Se₃ QSs with uniform shapes and sizes were obtained. The average lateral sizes of 2.7, 3.2, and 1.9 nm were derived for Bi₂Se₃ QSs, Sb₂Te₃ QSs, and TiS₂ QSs, respectively (Fig. 1(d) and Fig. S2, ESI†). Fig. 1(g) presents the high-resolution TEM (HRTEM) image and the corresponding fast Fourier transform (FFT) pattern of single Bi₂Se₃ QSs, indicating their single-crystalline structures. The lattice spacings of 0.23, 0.24, and 0.21 nm were revealed, corresponding to (101̄0̄), (101̄0̄), (102) crystal planes of Bi₂Se₃, Sb₂Te₃, and TiS₂, respectively (Fig. 1(g) and Fig. S2, ESI†). The average heights of 1.1, 1.2, and 0.7 nm were derived for Bi₂Se₃ QSs, Sb₂Te₃ QSs, and TiS₂ QSs, respectively (Fig. 1(e), (f) and Fig. S3, ESI†). The as-produced QSs were monolayers considering that the thicknesses of monolayer Bi₂Se₃, Sb₂Te₃, and TiS₂ were approximately 1, 1, and 0.6 nm, respectively.^18–20 Note that the individual height was acquired from the height profile of the single QS (Fig. 1(i)), which was the data source for the statistics in Fig. 1(f). Evidently, all the examined QSs were confirmed as quantum-sized monolayered structures.

Multiple spectroscopic techniques were utilized for further characterization of the as-produced QSs. Fig. 1(h) and Fig. S5 (ESI†) show the X-ray diffraction (XRD) patterns of the QSs. From Fig. 1(h), the characteristic peaks at 9.3, 18.6, 29.4, 40.3, 47.7, 57.6 and 68.9° correspond to (003), (006), (015), (101̄0̄), (116), (101̄6̄) and (102̄1̄) crystal planes of Bi₂Se₃.²¹ From Fig. S5a (ESI†), the characteristic peaks at 8.7, 17.4, 26.3, 28.2, 38.3, 44.6, 54.2, 63.2, and 74.8° were assigned to (003), (006), (009), (015), (101̄0̄), (101̄5̄), (101̄8̄), (102̄1̄) and (102̄4̄) crystal planes of Sb₂Te₃.²² From Fig. S5b (ESI†), the characteristic peaks at 15.5, 31.3, 34.2, 44.1, 47.8, 53.7, 57.6 and 65.5° were indexed to (001), (002), (101), (012), (003), (110), (103) and (004) crystal planes of 1T-TiS₂.²³ Compared with bulk layered materials, the as-produced QSs were identified with significantly reduced crystallinity and extremely enhanced edge states. The Raman spectra of the QSs are shown in Fig. 2(a), (d) and (g), where the insets schematically displayed the typical Raman vibrational modes. For Bi₂Se₃, as shown in Fig. 2(a), three characteristic peaks were observed in bulk and QSs. The peaks at 130.5 cm⁻¹ were assigned to E_g² modes, whereas the peaks at 172.7 cm⁻¹ corresponded to A_1g² modes.²⁴ Compared with bulk Bi₂Se₃, the Bi₂Se₃ QSs showed the E_g² modes and A_1g² modes with lower wavenumbers (i.e., 128.8 and 172.2 cm⁻¹, respectively), which could be related to the relatively free states of vibrations in quantum-sized Bi₂Se₃.²⁴ For Sb₂Te₃, as shown in Fig. 2(d), the peaks at 121.6 cm⁻¹ were assigned to E_u² modes, which could be infrared active.²⁵ The peaks at 139.3 cm⁻¹ were attributed to the vibrational modes of the Te–Te bonds²⁶ and the peaks at 165.7 cm⁻¹ were assigned to the A_1g² modes.²⁵ Compared with bulk Sb₂Te₃, the Sb₂Te₃ QSs presented greatly suppressed and notably blue-shifted (128.7 cm⁻¹) E_u² modes. Such unconventional blue-shift might be caused by the possible change of the topological structure/state (e.g., electronic and vibrational properties) when transforming the bulk into QSs. On the one hand, the quantum confinement effects could alter the topological properties of the as-produced QSs. For instance, the time-reversal symmetry could be disrupted by external perturbations or confinement potentials, resulting in localization of electronic states.²⁷ On the other hand, the geometric anisotropy of the as-produced QSs could affect the spin–orbit coupling of its surface/edge state, thus modifying the bulk-edge correspondence and the value of the topological invariant.²⁸ The main reason for the blue-shift in Raman spectra could be attributed to the coupling between surface/edge states and bulk states, as well as the emerging localized states.^29,30 For TiS₂, as shown in Fig. 2(g), three characteristic peaks located at 149.2, 200.2, and 333.8 cm⁻¹ were assigned to E_u, E_g, and A_1g modes, respectively, consistent with those reported previously.³¹ Compared with bulk TiS₂, the TiS₂ QSs demonstrated quite weak E_u modes at 147.3 cm⁻¹. The above-mentioned weakening of Raman signals could be originated from the extremely reduced lateral sizes and layer numbers when tailoring bulk layered materials into their QSs. The constituent elements and chemical states of the as-produced QSs were analyzed by X-ray photoelectron spectroscopy (XPS). Fig. S6 (ESI†) shows the XPS full spectra, where no impurities (e.g., Si from silica microspheres) were detected. Fig. 2(b), (c), (e), (f) and (h), (i) present the high-resolution XPS spectra, where both bulk and QSs were shown for comparison. For bulk Bi₂Se₃, as shown in Fig. 2(b) and (c), the two strong peaks at 158.2 and 163.5 eV corresponded to Bi 4f_7/2 and Bi 4f_5/2, while the two measured peaks at 53.6 and 54.4 eV were attributed to Se 3d_5/2 and Se 3d_3/2.³² For Bi₂Se₃ QSs, the Bi 4f peaks (159.7 eV for Bi 4f_7/2 and 165.0 eV for Bi 4f_5/2) and Se 3d peaks (55.2 eV for Se 3d_5/2 and 56.3 eV for Se 3d_3/2) all shifted towards higher binding energy by 1.5–1.9 eV. As reported previously,¹⁰ the extreme exposure of edge lattices/atoms in MoS₂ QSs would result in the XPS peak shifting towards lower binding energy. Therefore, the as-observed opposite shifting of the XPS peaks could be driven by the possible change of the topological structure/state in Bi₂Se₃ QSs. Similar trends were found in Sb₂Te₃ QSs and TiS₂ QSs. For bulk Sb₂Te₃, as shown in Fig. 2(e) and (f), the peaks at 528.6 and 538.0 eV were assigned to Sb 3d_5/2 and Sb 3d_3/2, while the peaks at 573.0 and 584.0 eV were attributed to Te 3d_5/2 and Te 3d_3/2. The probable oxidation of bulk Sb₂Te₃ led to the occurrence of the peaks at 530.4 eV for the Sb 3d_5/2 and 539.8 eV for the Sb 3d_3/2.³³ For Sb₂Te₃ QSs, the Sb 3d peaks (530.7 eV for Sb 3d_5/2 and 540.6 eV for Sb 3d_3/2) and Te 3d peaks (577.1 eV for Te 3d_5/2 and 588.8 eV for Te 3d_3/2) shifted towards higher binding energy by 2.1–2.6 eV and 4.1–4.8 eV, respectively. For bulk TiS₂, as shown in Fig. 2(h) and (i), the peaks of Ti 2p_3/2 and Ti 2p_1/2 were located at 456.3 and 462.5 eV. The two strong peaks at 160.9 and 162.1 eV corresponded to S 2p_3/2 and S 2p_1/2, consistent with those of 1T-TiS₂.²³ For TiS₂ QSs, the Ti 2p peaks (459.2 eV for Ti 2p_3/2 and 464.9 eV for Ti 2p_1/2) shifted towards higher binding energy by 2.9 and 2.4 eV, respectively. The S 2p peaks shifted towards higher binding energy as well, although great suppression of the XPS signal was observed.

Fig. 2 Spectroscopic characterization of the as-produced QSs. Raman spectra of (a) Bi₂Se₃ QSs, (d) Sb₂Te₃ QSs, and (g) TiS₂ QSs. High-resolution XPS spectra of (b), (c) Bi₂Se₃ QSs, (e), (f) Sb₂Te₃ QSs, and (h), (i) TiS₂ QSs. Data for bulk materials are shown for comparison.

The optical properties of the as-produced QSs were investigated, as shown in Fig. 3 and Fig. S7–S11 (ESI†). Fig. 3(a)–(c) present the excitation wavelength-, concentration-, and solvent-dependent PL behavior of the Bi₂Se₃ QS dispersions. A similar phenomenon could be found in the Sb₂Te₃ and TiS₂ QS dispersions (Fig. S8–S10, ESI†). From Fig. 3(a), the PL intensity reached the maximum at the excitation wavelength of 360 nm for the Bi₂Se₃ QS dispersions. Such excitation wavelength-dependent PL behavior could be attributed to the size/thickness heterogeneity of the 2D QSs.⁸Fig. 3(b) shows the concentration-dependent PL behavior of the Bi₂Se₃ QS dispersions. The PL intensity was progressively enhanced with the concentration from 0.001 to 0.025 mg mL⁻¹ because of the increase of the PL emitters. However, the PL intensity started to decrease with the concentration from 0.025 to 1 mg mL⁻¹, which could be ascribed to the aggregation-caused quenching (ACQ) mechanism.^8,34–36Fig. 3(c) presents the solvent-dependent PL behavior of the Bi₂Se₃ QS dispersions. The PL intensity of the QS dispersions in varying solvents showed remarkable difference, which could be determined by QS-solvent (direct) interactions.^8,37,38 The PL lifetimes and quantum yields of the QSs were measured, as shown in Fig. 3(d) and Fig. S11 (ESI†). The PL lifetimes of Bi₂Se₃, Sb₂Te₃, and TiS₂ QSs were measured to be approximately 6.6, 7.0, and 3.1 ns, respectively. The absolute quantum yields were measured to be 4.9, 3.6, and 6.3% for the Bi₂Se₃, Sb₂Te₃, and TiS₂ QSs at the wavelength of 360, 360 and 380 nm, respectively. It should be noted that all the examined QSs exhibited blue PL, which could be determined by their bandgaps. The optical bandgaps were derived from the UV-vis absorption spectra, as shown in Fig. S7 (ESI†). Fig. 3(e) compares the optical bandgaps between bulk and QSs. For Bi₂Se₃, Sb₂Te₃, and TiS₂, with the sizes down to 2.7, 3.2, and 1.9 nm, the bandgaps increased to 4.72, 4.69, and 3.59 eV, much larger than those (e.g., 0.22, 0.22, 0.30 eV) of bulk materials.^39–41 The as-produced QSs with extremely reduced thickness and lateral size would cause strong (out-of-plane and in-plane) quantum confinement effects, resulting in significant broadening of the optical bandgaps.^42,43 The bandgaps matched well with the blue emission of the QSs. Such (significant) bandgap-widening by (extreme) size-reduction would facilitate the practical applications of the topological insulators and semimetals.

Fig. 3 Photoluminescence of the QS dispersions. (a) Excitation wavelength-dependent PL behavior. (b) Concentration-dependent PL behavior. (c) Solvent-dependent PL behavior. (d) PL lifetimes and quantum yields. (e) Optical bandgap-modulation by size-reduction.

Not only linear but also nonlinear optical performances of the as-produced QSs were explored. Fig. 4(a) shows the schematic setup for the NSA measurements. The laser pulse with wavelengths of 532 and 800 nm, duration of 100 fs, and repetition rate of 1 kHz was incident on an aperture of diameter 4 mm. Fig. S12a (ESI†) presents the photographs of the pure PMMA and QSs-PMMA thin films (with the thickness of 120 μm and the edge length of 1 cm). The QSs-PMMA thin films with the fixed loading content of 0.1 wt% demonstrated slightly lower transparency than that of the pure PMMA, further confirmed by UV-vis absorption spectroscopy (Fig. S12b, ESI†). Such high transparency would be the basic requirement for future applications. Note that there was no detectable aggregation/orientation of the QSs in the hybrid thin films, which was determined by the thermodynamic stability of such dispersions.⁸ The NSA curves of the QSs-PMMA thin films are shown in Fig. S12c, d and S13 (ESI†). The normalized NSA curves (Fig. S13a and b, ESI†) were well fitted by the following formula: ⁴⁴ where α*(I) is the absorption coefficient, and are the saturable and nonsaturable absorption components, I is the peak intensity (or power density) of the incident pulsed laser, and I_s is the saturation intensity defined as the optical intensity required in a steady state to reduce the absorption to half of its unbleached value. Fig. 4(b) summarizes the as-acquired NSA performances of the Bi₂Se₃, Sb₂Te₃, and TiS₂ QSs-PMMA thin films. From Fig. 4(b), unprecedented NSA performances were achieved in the QSs-PMMA thin films at wavelengths of both 532 and 800 nm. At 532 nm, the absolute modulation depths of 71.6, 45.1, and 43.6% as well as the saturation intensities of 1.52, 0.82, and 1.53 MW cm⁻² (i.e., 152, 82, and 153 nJ cm⁻²) were derived for the Bi₂Se₃ QSs-PMMA, Sb₂Te₃ QSs-PMMA, and TiS₂ QSs-PMMA, respectively. At 800 nm, the absolute modulation depths of 72.4, 55.2, and 68.4% as well as the saturation intensities of 0.49, 0.34, and 0.80 MW cm⁻² (i.e., 49, 34, and 80 nJ cm⁻²) were achieved for the Bi₂Se₃ QSs-PMMA, Sb₂Te₃ QSs-PMMA, and TiS₂ QSs-PMMA, respectively. Note that the Bi₂Se₃ QSs-PMMA retained extremely high NSA performances in the visible region, while the Sb₂Te₃ QSs-PMMA and TiS₂ QSs-PMMA demonstrated wavelength-dependent NSA performances. In addition, the TiS₂ QSs-PMMA showed comparable NSA performances to those of the Bi₂Se₃ QSs-PMMA at 800 nm, indicating the great potential in both topological insulators and semimetals. Besides the absolute modulation depths and saturation intensities, the relative modulation depths (i.e., ) and nonsaturable losses (i.e., ) were derived, as shown in Fig. S13 (ESI†). All the examined QSs presented high and satisfactory . Particularly, the Bi₂Se₃ QSs-PMMA demonstrated ultrahigh of 95.9% and extremely low of 4.1%, further supporting its extraordinary NSA performances. Table S1 (ESI†) lists the NSA performances of the as-produced QSs and the topological insulators/semimetals from other works. Based on Table S1 (ESI†), the complete comparison of their NSA performances (i.e., the absolute modulation depths and saturation intensities) was accomplished, as shown in Fig. 4(c) and (d). Excitingly, ultrahigh nonlinear response and ultralow power excitation were simultaneously achieved in the as-produced QSs. Meanwhile, the Bi₂Se₃ QSs-PMMA demonstrated record-high absolute modulation depth (72.4% at 800 nm), which had never been achieved before (not limited to topological insulators/semimetals). Such extraordinary NSA performances of the as-fabricated QSs-PMMA thin films could originate from three aspects: (1) the inherent characteristics of the material; (2) intrinsic edge effects; and (3) quantum confinement effect. Firstly, topological insulator/semimetal were a novel state of quantum matter with an insulating bulk state and gapless surface/edge states.^45,46 The unique electronic structure at the surface/edge states of the topological insulator/semimetal made it different from the traditional saturable absorbers (such as graphene, hexagonal boron nitride, transition metal dichalcogenides, In₂X₃(X = S, Se, Te), MXene) thus exhibited higher NSA performances.^8,9,47,48 Therefore, the inherent characteristics of topological insulator/semimetal played an important role in the NSA performances. Secondly, the as-produced QSs possessed entirely exposed edges, maximizing their intrinsic edge effects (nonequilibrium situation (e.g., broken lattices, unsaturated/dangling bonds, dynamic changes, etc.) and asymmetric environment). The lattice at the surfaces/edges would dominate compared with their internal lattice in the as-produced QSs. The key roles of the rich surface/edge electronic states on the NSA performances included two aspects: (1) the unique density of states leaded to a strong overlap between the electronic wavefunctions and incident photons, resulting in an enhanced light–matter interaction. Such interaction facilitated the absorption of the incident light; and (2) the surface/edge electronic states of the as-produced QSs were topologically protected, indicating that they were robust against disorders and perturbations. The robustness of the surface/edge states ensured their effective nonlinear saturation absorption. Hence, the surface/edge (free, nonequilibrium) electronic states played a significant role in their absorption of photons.⁴⁹ Thirdly, the extreme size-reduction in the QSs would induce (both in-plane and out-of-plane) quantum confinement effects. Such effects would change the electronic structure, exciton properties and density of states of the as-produced QSs, directly affecting the changes of its nonlinear absorption coefficient, saturation intensity and excited state dynamics, resulting in ultrahigh saturable absorption.^50–52 Evidently, the combination of the inherent characteristics of the material, quantum confinement and intrinsic edge effects could be determinative to their phenomenal NSA performances of the quantum-sized topological insulators and semimetals.

Fig. 4 NLO performances of the QS solid thin films. (a) Schematic setup of the NSA measurement. (b) Plots of the absolute modulation depth and saturation intensity. (c) and (d) NSA performance comparison in topological insulators/semimetals. The references (S2–S27) are listed in Table S1 and the ESI.†

3. Conclusions

In summary, quantum-sized topological insulators/semimetals (i.e., Bi₂Se₃ QSs, Sb₂Te₃ QSs, and TiS₂ QSs) were produced via an all-physical top-down method. The as-produced QSs were monolayers with intrinsic characteristics, which could be determinative to their extraordinary performances. The highly stable QS dispersions presented excitation wavelength-, concentration-, and solvent-dependent PL. The highly transparent QSs-PMMA thin films demonstrated broadband NSA in the visible. Ultrahigh nonlinear response (72.4 and 68.4%) and ultralow power excitation (0.49 and 0.80 MW cm⁻²) were simultaneously achieved in both Bi₂Se₃ QSs-PMMA and TiS₂ QSs-PMMA. Compared with TiS₂ QSs-PMMA, Bi₂Se₃ QSs-PMMA maintained extremely high NSA performance at varying (laser) wavelength (532 and 800 nm). Such a highly desired broadband feature in quantum-sized topological insulators would undoubtedly facilitate their applications in mode-locked lasers and related fields.

Author contributions

Z. C. performed the experiments and characterization studies. Y. Z. supervised the research project. Y. Z. and Z. C. analyzed the data and wrote the manuscript. Z. L. and Y. L. helped with the spectroscopic characterization. X. S. and X. L. performed the nonlinear optical characterization.

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (no. 52073070, 21673054, 11874130, and 22073022), the Strategic Priority Research Program of Chinese Academy of Sciences (no. XDB36000000), the National Key R&D Program of China (no. 2018YFA0703700), and the DNL Cooperation Fund CAS (DNL202016).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3nh00282a

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