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Abstract
Looking for materials with compelling nonlinear optical (NLO) response is of great importance for next-generation nonlinear nanophotonics. We demonstrate an escalated two-photon absorption (TPA) in ultrasmall niobium carbide quantum dots (Nb2C QDs) that is induced by a two-even-parity states transition. The TPA response of Nb2C QDs was observed in the near-infrared band of 1064–1550 nm. Surprisingly, at 1064 nm, Nb2C QDs shows an enhanced TPA response than other wavelengths with a nonlinear absorption coefficient up to a value of 0.52 ± 0.05 cm/GW. Additionally, the nonlinear optical response of Nb2C changes to saturable absorption when the incident wavelength is between 400–800 nm wavelength. Density functional theory (DFT) validates that TPA, induced by two even-parity states transition, breaks the forbidden single-photon transition, enabling a tremendous TPA response in Nb2C QDs at 1064 nm. It offers the possibility of manipulating the NLO response of Nb2C via morphology or surface termination.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Two-photon absorption (TPA) was defined as the ground state electrons absorbing two photons and jumping to a higher-lying state through a virtual intermediate state [1]. Further, considering Laporte's electron transition rule, the different parity (odd to even or even to odd) between states is required for one-photon transition. The two-photon transition process can be interpreted as two successive single-photon transitions through an imaginary intermediate state. The essential transition selection rules become the same parity (odd to odd or even to even) between states [2] for two-photon transition cases. By manipulating the parity-forbidden transitions, optical absorption properties and photoluminescence of material can be well designed. Such a seminal idea has been demonstrated in improving the emission property of lead-free metal halide perovskites by Yan and Tang et al. [3,4]
Tremendous efforts have been involved in exploring TPA effects of the different materials and systems, including organic dyes [5,6], noble metal nanoparticles and nanoclusters [7], metal-organic frameworks [8], nanocrystals [9], and carbon-based nanomaterials (fullerene, carbon tube, graphene) [10], etc. At the same time, potential applications of TPA have been demonstrated in bio-imaging [11], laser protection (optical limiting) [10], cancer photodynamic therapy [12], etc. The exploration of low dimensional material-based TPA can also achieve significant nonlinear performance and emerging potential applications, such as black phosphorus [13,14], transition metal dichalcogenides (TMDs) [15,16], 2D perovskite [17], carbon dots [18–20], and others [21,22].
Low dimensional transition metal carbon-nitrogen compounds, termed MXene, are rising stars of the 2D material world [23,24]. The general formula of MXenes can be expressed to be Mn+1Xn (where M = Sc, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, etc., and X = C or N or both) [25]. The large MXene family shows wide potential applications, including energy storage [26], harvesting [27], electrocatalysis [28], biomedical and environmental research [29]. The ultrafast nonlinear optical properties of MXene were also investigated, which showed typical saturable absorption [30,31], spatial self-phase modulation [32–34], and harmonic generation [35]. Recently, TPA in monolayer Ti2C3 induced by parallel band absorption effect was reported, suggesting promising potential optical limiting and light modulation [36]. In recent work, we observed a similar property of Nb2C with typical TPA at the optical communication band [37].
Here, we reported two even-parity states transition induced enhanced two-photon absorption in ultrasmall niobium carbide quantum dots with an average transverse size of 2.4 ± 0.7 nm and a thickness of 2.1 ± 0.6 nm. The Nb2C QDs were synthesized via the widely used selective-etching-assisted liquid exfoliation method. Intriguingly, an enhanced two-photon absorption response of Nb2C QDs at 1064 nm wavelength was demonstrated compared to that of other wavelengths with TPA response. This enhanced TPA effect can be attributed to a new two-photon transition channel between two even-parity states in Nb2C QDs, confirmed by our density functional theory (DFT) calculations. Compared to the nonlinear optical results in the Nb2C nanosheets, nonlinear optical response inversion (a shift from saturable absorption to two-photon absorption) wavelength of Nb2C QDs blue shift to a shorter wavelength. Present results suggest that by rational constructing and designing the MXene structure, the nonlinear optical response, including the TPA effect of MXene, can be obtained as required, which is induced by odd-even-parity states regulation. Such TPA response can be significant in developing the MXene based optical modulation elements such as optical limiters and optical diodes.
2. Preparation and characterizations of MXene niobium carbide quantum dots
The MXene was fabricated with the conventional selective-etching-assisted liquid exfoliation method (See Methods section in Supplement 1). Figures 1(a), (b) depict the morphology images of Nb2C QDs obtained by transmission electron microscopy (TEM). The Nb2C MXene demonstrated a morphology as the ultra-small quantum dots with uniform distribution. Figure 1(c) shows the AFM image of Nb2C QDs. The height profile (Inset of Fig. 1(c)) corresponding to the solid white line confirmed the nanometer thickness of prepared Nb2C QDs. As per statistical analysis in Fig. 1(d), (e), the average lateral size of Nb2C QDs is about 2.4 ± 0.7 nm, and the average thickness of Nb2C QDs is determined to be 2.1 ± 0.6 nm. Figure 1(f) shows the vis−NIR spectra of Nb2C nanosheets (NSs) and Nb2C QDs in an aqueous solution. Typical resonance absorption near-infrared band [37] existed in both Nb2C NSs and Nb2C QDs. Interestingly, the distinct absorption peak at the visible region of absorption spectra of Nb2C QDs can be observed, which is attributed to the size-dependent effect of Nb2C QDs. Figure 1 (g) shows X-ray photoelectron spectroscopy (XPS) of Nb2C QDs and MAX phase Nb2AlC. Both contain all possible elements, such as Nb, C, and a limited amount of O. Compared to the MAX phase Nb2AlC, the Nb2C QDs XPS spectra do not include the apparent peak of Al 2s and Al 2p, suggesting that HF has successfully etched Al element. Figures 1 (h), (I), and S2 show the details of high-resolution XPS scanning for Nb, F, Al, and O elements. As shown in Fig. 1 (h), the binding energies for the Nb-C 3d3/2 and Nb-C 3d5/2 are located at 204.8 eV and 202.2 eV, respectively. The existence of the Nb-O bond at 205.5 eV indicates the formation of niobium oxide or surface oxygen group. The characteristic band of F 1s is at 683.7 eV, confirming the presence of F termination at the surface of Nb2C QDs (Fig. 1(i)). Further, high-resolution scanning of the Al element confirms that the Al element is removed during the selectively acid etching processing. Fig. S1(a) shows the result of high-resolution scanning of the Al element. The presence of Al in MXene weakens or disappears, confirming Al element removal after the selectively acid etching processing. Moreover, the XPS scan of O 1s state have indicated the C-Nb-OH and Nb-O bonds, which proves the existence of the hydroxyl groups on the surface of Nb2C QDs (Fig. S1(b)). Therefore, the XPS spectra of Nb2C QDs demonstrated the removal of Al element and the appearance of -F, -O, and -OH surface groups. As shown in Fig. S2, the MAX phase Nb2AlC Raman spectra, the prominent peaks at 130 cm−1, 182 cm−1, 205 cm−1, and 261 cm−1 correspond to $\textrm{E}_{2\textrm{g}}^1$, $\textrm{E}_{2\textrm{g}}^2$, ${\textrm{E}_{1\textrm{g}}}$ and ${\textrm{A}_{1\textrm{g}}}$ vibrational modes, respectively. It is evident that the Al atom related vibrational modes $\textrm{E}_{2\textrm{g}}^2$ and ${\textrm{E}_{1\textrm{g}}}$ are suppressed or disappeared in the Raman spectra of Nb2C QDs [38]. The Raman results have also confirmed the appearance of the MXene phase. Fig. S3 shows the fluorescence spectrum of Nb2C QDs. The Nb2C QDs demonstrated a strong and broadband emission with a centered at 539 nm. Compared to previous reports, a red shift of fluorescence spectrum can be observed which may be attributed to different size and surface defects [39].
Fig. 1. Characterizations of Nb2C QDs. (a) and (b) TEM images of Nb2C QDs under different magnification. (c) AFM image of Nb2C QDs. Inset: height profile corresponding to solid white line 1 in Fig. 1(c). (d) Statistical analysis of the lateral size of 200 Nb2C QDs. (e) Statistical analysis of the height of 200 Nb2C QDs. (f) UV-vis absorption Nb2C nanosheets and Nb2C QDs. (g) X-ray photoelectron spectroscopy (XPS) of Nb2C QDs and Nb2AlC powder. (h) XPS precise scan of F 1s. i) XPS accurate scan of Nb 3d.
3. Results and discussion
Figure 2(a)-(f) shows the OA Z-scan (See Methods section in Supplement 1) results of Nb2C QDs at 400, 620, 800, 1064, 1240, and 1550 nm under variable light intensity. Nb2C QDs exhibits saturable absorption (SA) response at 400, 620, and 800 nm. The optical limiting (OL) response was observed when the incident laser wavelength changed to the infrared band at 1064, 1240, and 1550 nm. Such an inverted nonlinear optical response has been reported in previous work [37], which can be well explained by the parallel band absorption effects induced by TPA. Unlike those reports, the nonlinear optical response inverted wavelength changes to near-infrared 1064 nm with a significantly enhanced TPA response compared to the other wavelengths. The fundamental mechanism will be discussed in the following section in detail.
Fig. 2. Open-aperture (OA) Z-scan results of Nb2C QDs under different excitation intensities of different wavelengths: (a) 400 nm, (b) 620 nm, (c) 800 nm, (d) 1064 nm, (e) 1240 nm, (f) 1550 nm.
Next, we further extract nonlinear optical parameters of Nb2C QDs, including nonlinear absorption coefficient αNL, third-order nonlinear optical susceptibility $Im{\chi ^{(3 )}} = \frac{{{{10}^{ - 7}}c\lambda n_0^2}}{{96{\pi ^2}}}{\alpha _{NL}}$ and figure of merit ($FOM = \; \mathrm{\mid }Im{\chi ^{(3 )}}/{\alpha _0}\mathrm{\mid }$) [40], at different wavelengths and excitation intensity. According to the nonlinear optical theory [41], the raw data curve in Fig. 2 is fitted by the following equation:
Fig. 3. Analysis of nonlinear optical parameters of Nb2C QDs at different wavelengths. (a) The nonlinear absorption coefficient, (b) the Imaginary part of the third-order nonlinear susceptibility, (c) figure of merit (FOM) of Nb2C QDs depending on the excitation wavelength. (d) Plots of Ln(1-T) vs. Ln(I) at different wavelengths; the scatters are experimental data, and the solid lines are the fitting lines; s represents the slope of the fitting line.
Table 1. Linear and nonlinear optical parameters of Nb2C QDs and other materials (NAR: Nonlinear Absorption Response)
Different nonlinear optical responses at various excitation wavelengths indicated that the dominant mechanism of nonlinear optical response has fundamentally changed. In Fig. S4, the change of transmittance ΔT was extracted as a function of incident intensity in a different wavelength. The ΔT shows the linear dependence on the incident intensity at each wavelength, proving that the NLO response dominated the Z-scan signals. Moreover, it is evident that the slope at 1064 nm is larger than the other wavelength; the reason will be discussed later. At the visible region (400 nm and 620 nm) and near-infrared band (800 nm), the saturable absorption of Nb2C QDs is induced by optical bleaching. This type of optical bleaching effect has been investigated extensively in the 2D material system and was widely used as a saturable absorber in passive laser mode-locking applications [42,43]. The saturable absorption intensities ${I_s}$ is determined by the following equation [44]:
where ${A_s}$ represents the modulation depth, and ${A_{ns}}$ represents the non-saturable components. By fitting the data in Fig. S5a with Eq. (2), we can determine the saturation intensity Is. The fitting results are shown in Fig. S5b. The saturation intensity ranges from 82 to 194 GW/cm2, close to the other 2D materials [37,40]. The optical limiting (OL) effects at 1064, 1240, and 1550 nm are shown in Fig. S6a-c. The OL threshold (${I_{th}}$) can quantitatively describe the characteristics of the OL effect which refers to the input fluence when the normalized transmittance drops by 50%. The parameters related to OL can be seen in Table 1. Among them, the OL threshold at 1064 nm is minimum.In Fig. 3(d), by plotting the Ln (1-T) as a function of Ln (I), the slope of the curve can be used to distinguish the multiphoton absorption process in the nonlinear optical response (s = 1 for TPA). The TPA effect dominates the nonlinear optical response of Nb2C QDs at 1064 nm, 1240 nm, and 1550 nm wavelengths. Overall, there are two main novel phenomena in the present results. Firstly, as noted above, there is an obvious inverted NLO response of Nb2C QDs at 1064 nm wavelength. That is different from our previous report in Nb2C nanosheets [37], in which inverted NLO response occurs at 1550 nm (Fig. S7). Secondly, the TPA-induced OL effects of Nb2C QDs exhibit marvelous enhancement at 1064 nm wavelength. It has excellent potential for actively regulating the nonlinear optical response of Nb2C QDs to understand the fundamental physical mechanism of these new phenomena.
The DFT calculation was employed to investigate the possible fundamental mechanism behind this phenomenon to reveal the interesting size-dependent effects of inverse NLO response and significantly enhanced TPA at 1064 nm wavelength. Due to the hydrofluoric acid treatment, Nb2C QDs terminated by different functional groups such as - OH, - O, and - F [45]. That can also be confirmed by the XPS characterization results of prepared Nb2C QDs. To simulate the experimental environment, the Nb2C QDs terminated with - F and - OH have been calculated, respectively.
The calculated optical absorption spectra of Nb2CT2 (T = F, OH) with various sizes are depicted in Fig. 4(a)-(b). The absorption edge within the experimental photon energy range (0.5–2.5 eV) is fitted by the black dashed line. These results further prove the parallel band absorption effects in metallic MXenes [36,37,46]. In addition, the absorption edge of Nb2CF2 and Nb2C(OH)2 drops with the increase in lateral size (Fig. 4(c)-(d)), showing the decreasing photon energy at the inversion point with the rising lateral size of Nb2C (Fig. S7). It means the exciting photon energy of 1.16 eV (1064 nm) and 1 eV (1240 nm) exceeds the absorption edge of Nb2C nanosheets but is below the absorption edge of Nb2C QDs. Thus, the first case exhibits saturable absorption NLO response while the latter exhibits TPA-induced OL effect, and both of them are consistent with the experimental results. Similar size-dependent nonlinear optical effects have been reported in other quantum dots systems, such as CdTe QDs [47], Graphene QDs [48], and CdS QDs [49]. These size-dependent NLO responses of Nb2C low-dimensional materials offer an opportunity for their applications in laser protection and all-optical modulation devices.
Fig. 4. Optical absorption spectra of Nb2CT2 (T = F, OH) with various sizes. The black dashed lines were used for an approximate linear fit to estimate the band edge for the absorption peak within the energy range of 0.5 ∼ 2.5 eV [58]. (c, d) The absorption peak of different sizes of Nb2C QDs, dropping with the increase in lateral size.
Another interesting result is that the TPA-induced OL effects of Nb2C QDs show a remarkable enhancement at 1064 nm wavelength. The DFT calculated band structure and transition selection rule explain the unusual enhancement effect at 1.16 eV. When considering the optical absorption from the first principle, the frequency-dependent absorption can be expressed as Eq. (3) [50]:
The two-photon induced optical transition involves different transition selection rules compared to single-photon transition [41]. Since the two-photon process can be interpreted as two successive single-photon transitions through a virtual intermediate state, it is reasonable to derive that the two-photon transition is allowed when the initial state and final state are of the same parity [54]. It means the two-photon transition process could break the single-photon transition restriction, which is induced by symmetry. At the same time, the strength of the two-photon transition depends on the JDOS [55,56], which means the two-photon transition is also more preferable in the three types of van Hove singularities at symmetry points.
Figure 5(a) and 5(d) exhibit the band structures of Nb2CF2 and Nb2C(OH)2, respectively. The previous results [33,41] show that Nb2CF2 and Nb2C(OH)2 are metallic since the electronic band crosses the Fermi level. To analyze the band symmetry, the structure symmetry (hexagonal, $p\bar{3}m1$ space group) of Nb2CF2 and Nb2C(OH)2 are kept during the calculation [57]. In Fig. 5(a), it can be seen that the bands in the solid black rectangle's high region have the characteristic of van Hove singularities at Γ symmetry point (maximum point, minimum point, and saddle point), which contribute enormously for photon transition. From the right panel of Fig. 5(a), it can be seen that the valence bands 20 and 21 exhibit the even parity (Γ3+), and the conduction band 22 indicates an odd parity (Γ2-). In contrast, the conduction bands 23 and 24 exhibit even parity (Γ3+). Hence, there is parity-forbidden (even to even or odd to odd) [3] transition between valence bands 20, 21 and conduction bands 23, 24. The calculated transition dipole moment in Figs. 5(a) and 5(b) proves the parity symmetry analysis. The transition from 20 and 21 to 22 has a large TDM around the Γ point, while the other has near-zero TDM. In Fig. 5(c), the TDM value and energy difference of each possible transition between two bands at the Γ point are compared. Intuitively, the transition from 20 and 21 to 22 is parity allowed where the others are forbidden single-photon transitions with allowed two-photon transitions. As shown in Fig. 5(d)-(f), the optical transition of Nb2C(OH)2 exhibits an analogous process. Due to the modulation of termination, the band index 24 of Nb2C(OH)2 is above the fermi level at Γ point, while the other bands are below the Fermi level (Fig. 5(d)). Thus, there are four possible transitions between two states where the transition from band 23 to 24 is parity allowed (Fig. 5(e)). There is a conversion from single-photon transition to two-photon transition (Fig. 5(f)) with increased photon energy. Regarding photon energy, the exciting laser with single-photon energy of 2.06 eV is parity allowed, while the exciting laser with single-photon energy of 2.37 eV is forbidden. Once two photons offer the transition energy of 2.37 eV, this parity forbidden has been broken to provide enormous states for two-photon transition. The optical transition of Nb2CF2 in Γ point is shown schematically in Fig. 6.
Fig. 5. DFT + U calculated band structures and TDM of Nb2CT2 (T = F, OH). (a, d) The band structure of Nb2CF2 and Nb2C(OH)2 indicates the irreducible representation in Γ point by Koster notations. The right panel is the amplification of the Γ point near the Fermi level; the number indicates the band index. (b, e) Calculated TDM of Nb2CF2 and Nb2C(OH)2 between the possible bands in the amplification area. (c, f) Left: TDM at Γ points between two possible bands of Nb2CF2 and Nb2C(OH)2. Right: The energy difference of corresponding bands at Γ points. The light red area represents the single-photon transition allowed between two bands at Γ point, while the light blue area indicates the single-photon forbidden transition with an allowed two-photon transition.
Fig. 6. Schematic diagram of optical transition of Nb2CF2 in Γ point. No parity is forbidden under the excitation of the relatively low photon energy of 2.06 eV (left panel); the single-photon transition is allowed. A single-photon transition is prohibited when the excitation photon energy becomes 2.37 eV (middle panel); the initial and final states exhibit an even parity (Γ3+). Once the transition energy is offered by two photons (right panel), this parity forbidden has been broken. Because the two-photon transition process can be interpreted as two successive single-photon transitions through an imaginary intermediate state, the two-photon transition is allowed between states of the same parity.
Based on the above discussion of calculation results, we can construct the physical picture of experiments as follows. Since two types of Nb2CF2 and Nb2C(OH)2 coexist in the experimental solution, the average effect can make the observed and calculated values slightly different. When the photon energy of the excitation laser exceeds the optical absorption edge (1.16–1.55 eV), the saturable absorption induced by Pauli blocking effects dominated the NLO response of short wavelength (400–800 nm). If the single-photon energy is below the optical absorption edge, the OL induced by two-photon absorption dominated the NLO response of long-wavelength (1064–1550 nm). During the conversion from the edge of single-photon absorption (1.55 eV, 800 nm) to the edge of two-photon absorption (1.16 eV, 1064 nm), there is a step type change in the transition energy (1.55 eV to 2.32 eV) which means that these two processes occurred between different states. In the case of 1064 nm, see the right panel of Fig. 6. The two-photon transition energy of 2.32 eV resonates with abundant JDOS and has no parity forbidden transition (even to two-photon transition), which causes enhanced OL effects. While the excitation photon energies are below 1.16 eV, as in the cases of 1240 nm and 1550 nm, their two-photon transition energies (2 eV and 1.6 eV) are below the two-photon resonance energy range, which causes the normal TPA induced OL effects.
4. Conclusion
We successfully prepared the Nb2C QDs with a lateral size of 2.4 ± 0.7 nm and an average thickness of 2.1 ± 0.6 nm. The NLO absorption properties of Nb2C QDs were determined through an OA Z-scan experiment. It exhibited the typical saturable absorption response within the 400–800 nm spectral range, while the OL response demonstrated in the near-infrared band of 1064–1550 nm. Compared to Nb2C nanosheets, the significant blue shift of inversion points in Nb2C QDs was observed and attributed to the size-dependent effects and confirmed by DFT calculation. At the wavelength of 1064 nm, particularly, the nonlinear absorption coefficient of Nb2C QDs was revealed to be 0.52 ± 0.05 cm/GW, which was significantly larger than those at the other wavelengths. This enhanced TPA response at 1064 nm was attributed to a new two-photon transition channel between two even-parity states which is not fit for the other two-photon transitions having lower photon energies. We have demonstrated the possibility of manipulating the NLO absorption response of Nb2C MXene via morphology or surface termination, which enables their applications in NLO devices. More generally, discovering enhanced TPA response in Nb2C QDs through two even-parity states transition will enlighten the construction of NLO material.
Funding
National Natural Science Foundation of China (11904239, 61874141, 61875232); China Postdoctoral Science Foundation (2021M690169); Natural Science Foundation of Hunan Province (2021JJ40709); Postgraduate Innovative Project of Central South University (160171007, 2021zzts0504).
Disclosures
The authors declare no competing financial interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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