Abstract
This work reports the real-time observation of the interlayer lattice vibrations in bilayer and few-layer by means of the coherent phonon method. The layer-breathing mode and standing wave mode of the interlayer vibrations are found to coexist in such a kind of group-10 transition metal dichalcogenides (TMDCs). The interlayer breathing force constant standing for perpendicular coupling (per effective atom) is derived as 7.5 N/m, 2.5 times larger than that of graphene. The interlayer shearing force constant is comparable to the interlayer breathing force constant, which indicates that has nearly isotropic interlayer coupling. The low-frequency Raman spectroscopy elucidates the polarization behavior of the layer-breathing mode that is assigned to have symmetry. The standing wave mode shows redshift with the increasing number of layers, which successfully determines the out-of-plane sound velocity of experimentally. Our results manifest that the coherent phonon method is a good tool to uncover the interlayer lattice vibrations, beyond the conventional Raman spectroscopy limit. The strong interlayer interaction in group-10 TMDCs reveals their promising potential in high-frequency () micro-mechanical resonators.
© 2019 Chinese Laser Press
1. INTRODUCTION
It is well known that for two-dimensional (2D) materials, the interlayer interaction is vitally important for the layer-dependent properties, such as band structure, carrier mobility, and thermal conductivity. , as one of typical group-10 transition metal dichalcogenides (TMDCs), undergoes a dramatical bandgap shrinking from an indirect bandgap semiconductor for monolayer () to a semimetal for bulk [1–6], which is expected to be a promising candidate in homogeneous interconnection electronic circuits [7]. The sharp decline of the bandgap with increasing layer thickness in implies that the interaction between adjacent layers might be very large, which is desirable for future device application like high-frequency [terahertz ] micro-mechanical resonators [8]. The interlayer interactions can be reflected via detection of interlayer lattice vibrations. Raman spectroscopy is a general method to observe lattice vibrations [9,10]. Although the low-frequency Raman spectroscopy can determine some relatively high interlayer vibrational modes, the ultralow phonon modes (e.g., 10–23 L in this work) that are vital for studying interlayer coupling will be immersed in the laser line due to the limit of the optical filter in Raman spectroscopy. Here, by utilizing the ultrafast pump–probe technique [11], we observe the real time dynamics of two interlayer coherent acoustic phonon modes coexisting in bilayer and few-layer . The THz layer-breathing mode (LBM) is in consistence with our low-frequency Raman spectra, while the standing wave mode (SWM), Raman inactive, is observed directly in group-10 TMDCs. The contribution of the adjacent unit cell to the interlayer interaction can be derived from the LBM, proving that indeed owns strong interlayer van der Waals force, much larger than graphene. Meanwhile, we obtain the out-of-plane sound velocity of experimentally from the SWM, in good agreement with the theoretical calculations [12,13].
2. CHARACTERIZATIONS AND PUMP–PROBE EXPERIMENT
Large-scale continuous thin films with different layers were synthesized on sapphire substrate by chemical vapor deposition (CVD) growth as described previously [14], and the size of the samples was approximately (Sixcarbon Tech, Shenzhen, China). adopts an octahedral structure (1T phase) in the AA arrangement of stacked layers and belongs to the space group [15]. The number of layers determined by atomic force microscopy (AFM) is 2, 5, 8, 10, 15, 17, and 23 L, respectively, as shown in Figs. 1(a)–1(c) and Appendix A. The Raman spectra from to under 532 nm excitation are shown in Fig. 1(d). All the samples show two clear intralayer peaks, and modes. The mode originates from the in-plane vibration of Se atoms and the mode corresponds to the out-of-plane vibration of Se atoms. In addition, there is a rather weak intralayer longitudinal optical (LO) mode, which is the combination of the in-plane and out-of-plane modes from the vibrations of Pt and Se atoms in opposite phase. The peak positions of the three modes are extracted and plotted in Fig. 1(e), which indicates that the mode has a slight redshift around with increasing film thickness and the mode is almost pinned at , along with the nearly unchanged LO mode. The intensity ratio in Fig. 1(f) keeps on growing from 2 L to 23 L. The peak positions and the tendency of intralayer Raman shifts are in agreement with previous results [3,16,17]. The absolute linear absorptions from 400 nm to 1100 nm were derived from the formula in the same way as and [18]. The linear transmission (T) and reflection (R) spectra are shown in Appendix A. We can calculate the linear absorption coefficient with [19] and the specific data are listed below. Meanwhile, the layer-dependent Tauc plots derived from the absorption spectra verify that with 2–23 L undergoes a transition from semiconductor to semimetal, as shown in Fig. 1(g).
A setup of degenerate noncollinear ultrafast pump–probe spectroscopy was home-built for studying coherent phonons (CPs). The ultrafast laser produced 380 fs pulses at a photon energy of 1.19 eV (1040 nm) with the repetition rate of 100 kHz. These pulses were split into pump and probe beams with orthogonal polarization in order to eliminate mutual interference. The pump and probe beams are focused on the sample, and the focused spot sizes are 107 μm and 31 μm, respectively. To investigate the layer dependence of CPs in layered , we measured the time-resolved differential transmission signals of 2, 5, 8, 10, 15, 17, and 23 L samples, covering the transition of semiconductor to semimetal. with 15 layers (15 L-) was taken as an example, as shown in Fig. 2(a). It includes two components: incoherent carrier dynamics and CP dynamics. (1) The increased transmission before the zero delay point is owing to the band filling effect as the bandgap of 15 L- [nearly zero in Fig. 1(g)] is much smaller than the excitation photon energy (1.19 eV). After the zero point, the excited carriers first relax fast to reach a state with , and then a subsequent absorption process appears, followed by typical carrier relaxation dynamics in several hundred picoseconds, which has been studied in our previous work [20]. (2) Damped oscillations generated by CPs are superimposed on the relaxation process. From Fig. 2(a), the CP oscillation modulates the transmission initially by approximately 28%, much larger than that of (group-6 TMDCs) and graphite [21–24], indicating that the contribution of CPs in is very large and is even comparable to that of excited carriers.
3. RESULTS AND DISCUSSION
The inset of Fig. 2(a) shows the fast Fourier transform (FFT) of the damped oscillation. It is obvious that there are two vibrational frequencies (0.15 THz and 0.05 THz). It means that the experimental data should be fitted with a two-exponential model including two decaying sinusoidal wave functions [25–27]:
in which is the delay time between pump and probe pulses. The exponential terms marked by footnote depict the fast and slow relaxation processes of the excited carriers. The two sinusoidal decays describe the damped oscillations, where the amplitude , the decay time , the frequency , and the initial phase of two different oscillation modes are marked by footnote . The pure damped oscillation signal was extracted by subtracting the red curve from the black one, as shown in Fig. 2(b) (green curve). It can be seen that the damped oscillation can be decomposed into two separate modes: the higher-frequency mode 0.15 THz (Mode 1, yellow) and lower-frequency mode 0.05 THz (Mode 2, blue).The CP oscillations of with other different layers (2, 5, 8, 10, 17, and 23 L) were extracted in the same way, as shown in Fig. 2(c). Figure 2(d) summarizes the layer-dependent FFT results of the oscillations of all samples. Mode 1 varies from 0.78 THz for 2 L to 0.10 THz for 23 L, while Mode 2 softens from 0.24 THz to 0.03 THz. Both of them show a typical redshift with the increment of the number of layers. The detailed values of the frequencies (in the units of THz, , and picosecond) are listed in Table 1.
For 2D layered materials, lattice vibrations contain high-frequency intralayer vibrations and low-frequency interlayer vibrations. In view of the frequency range in our experiment, it is reasonable to deduce that Mode 1 and Mode 2 should originate from interlayer vibrations, which is in accordance with the following theoretical analysis. Interlayer vibrations can be divided into the out-of-plane LBM, in-plane shear mode, and propagating wave mode [21,28,29]. The LBM is the interlayer motions perpendicular to the plane, corresponding to mode in Raman spectra, and the shear mode is parallel to the plane, corresponding to and modes [28]. It was noted that many interlayer vibrational modes of were Raman active [4,30]. In order to identify the CP oscillation modes, we conducted the low-frequency Raman spectroscopy. Figure 3(a) shows the Raman spectra of 2 L-, 5 L-, and 8 L- from to under the excitation of 532 nm wavelength (Renishaw inVia Raman Spectroscope). Its spectral resolution is and the cutoff band of the high-pass filter is from to . It can be found in Fig. 3(b) that the Raman peak positions are in good consistency with the frequencies of Mode 1. For an -layer material, it has kinds of LBMs and shear modes because each layer vibrates in different amplitudes and opposite directions. As a result, there are fan-like branches of the LBMs and shear modes with the increasing number of layers, as shown in Fig. 3(b). These gray squares indicate the theoretical calculation of the LBMs in on the basis of density functional perturbation theory (DFPT) [4]. We can see that the values and tendency of Mode 1 are very close to the lowest branch of LBMs, which is also Raman active. Thus, in good agreement with both Raman spectra and DFPT calculations, CP oscillation of Mode 1 can be identified as the lowest LBM interlayer vibration in , which corresponds to the motion that the top half and the bottom half of the layers vibrate collectively but in the opposite phase [28,29]. The diagram of the vibrations varying with the number of layers is shown in Fig. 4. Other peaks in 5 L and 8 L in Fig. 3(a) were attributed to higher branch of LBMs. The frequencies of thicker samples were cut by the filter and unable to be detected. In addition, we also studied the polarization behavior of the phonon modes, as shown in Fig. 3(c). The amplitude of Mode 1 of 2 L- varies periodically with the polarization of the incident light. The polarization dependence of intralayer (in-plane) and (out-of-plane) modes is compared in Fig. 3(d). We can find that the polarity of Mode 1 is the same as the intralayer mode. Accordingly, as an out-of-plane mode, it is assigned to have the symmetry [31]. Thus, the amplitude of Mode 1 can also be fitted with , where is the intensity of the Raman peak, is a Raman tensor element, and is the angle between the polarization of the incident and scattered light [32]. In comparison, the amplitude of the mode in Fig. 3(d) is independent on the polarization of the incident laser and can be fitted by , where is another Raman tensor element [32].
The frequency of Mode 1 of each sample is extracted from Fig. 2(d) and plotted in the unit of in Fig. 5(a). For the LBM, in the one-dimensional linear atomic chain model [28,33,34], relative movement between intralayer atoms is neglected. Each layer is moving as a unit and each unit vibrates only in the direction (perpendicular to the plane). We can imagine interlayer interaction as a spring to connect the adjacent unit. Accordingly, the linear atomic chain model that considers merely the interlayer interaction between nearest neighbors was used to fit the data, as expressed in the formula
where represents the associated vibrational frequency for samples with different number of layers , the interlayer force constant between the nearest neighbors is a fitting parameter, is the speed of light, and the mass per unit area is . is just an index () and it is assigned to be 2 here because Mode 1 is the lowest branch as we have just mentioned. The fitting result is shown in Fig. 5(a) and the good agreement suggests that the interlayer interactions are dominated by the interactions between the nearest-neighboring layers. Because each layer vibrates in the direction that we have just mentioned, the fitted interlayer breathing force constant (IBFC) represents the interlayer interaction in direction , , while the IBFC of graphene [31] is larger, which seems that interlayer coupling of graphene is stronger than that of . But actually, we have to consider that graphene is a planar structure and each carbon atom plays a role in the interlayer interaction [28]. However, has a trigonal structure (1T phase) and only half of the Se atomic layer contributes to the nearest-neighboring interaction. If we make an approximation that the contribution of each Se atom is equal, the IBFC per effective atom comes out to be , which is 2.5 times larger than that of graphene (3 N/m [28]). It reveals that indeed has stronger interlayer interaction than graphene, which also explains its harder mechanical exfoliation. Furthermore, the good fitting result suggests that the force constant remains almost unchanged within the margin of error as the thickness is increasing, which implies that the softening of the phonons is not due to the change of interlayer coupling, but due to the increased number of layers [35]. The interlayer shear force constant (ISFC), , was calculated based on the data in Ref. [4]. It is also larger than that of [29], [29,36], graphene [37], and black phosphorus (BP) [28], which can be explained by the existence of quasi-covalent bonds between adjacent layers [32]. The IBFC and ISFC of are comparable, standing for the nearly isotropic interlayer coupling in , different from the anisotropic one in , , graphene, and BP. It is noteworthy that the frequency of the LBM shows an obvious dependence on the number of layers. As Raman spectroscopy is unable to determine the ultralow frequency (), the study of interlayer LBMs in CP oscillations widens the way to characterize the number of layers for 2D materials.The frequencies of Mode 2 are extremely low and mismatch any value in the LBMs and shear modes [4]. Figure 5(b) shows that the periods of Mode 2 vary linearly with the thickness, which is a typical feature of SWM [21]. The phenomenon can be explained by the generation of standing wave, which has been studied in many materials [21,38–40]. The thin film partly absorbs the pump pulse and produces electrons and holes. Electrons will transfer excess energy to the lattice by electron–phonon collisions during the relaxation to the band edge, resulting in an acoustic pulse. Then the acoustic phonons produce a negative elastic stress force [40], leading to a nuclear motion around the new equilibrium position just like a standing wave, which changes the lattice constants of periodically. Figure 4 shows the diagram of the vibrations with the increasing number of layers. The acoustic wave bounces back and forth inside the film, and modulates the bandgap of the film and hence the absorption of the probe beam periodically [38]. We can estimate the penetration depth [40], where is the linear absorption coefficient listed in Table 2. The calculated depth of each film is larger than the actual thickness of the corresponding film. For example, the penetration depth of 15 L- is 22.09 nm, larger than its thickness of 8.98 nm, which means that the stress force can act on the whole film rather than only the external surface. The vibrations in few-layer are relatively strong so that is expected to be applied in a micro-mechanical resonator, surface cleaning, and driving motor, etc. [8,41,42].
According to the standing wave conditions, the laser is incident on the free surface of the sample (the zero-stress boundary condition), and the other surface of the sample is limited by the sapphire substrate (the zero-displacement boundary condition) [21,38–40]. Then, the period of the oscillation can be defined as
where is the thickness of the film, and is the out-of-plane sound velocity. The values of the oscillation period are listed in Table 1. The sound velocity, , of can be derived from the slope of Fig. 5(b), in the same order of magnitude as the theoretical calculations in Refs. [12,13]. To the best of our knowledge, this is the first time to determine the sound velocity in layered experimentally. Although undergoes a phase transition from semiconductor to semimetal as the number of layers varies from 2 L to 23 L, the oscillation periods do not show any discontinuity. It is reasonable as the lattice structure of remains almost unchanged in spite of its transition. We also note that no acoustic echo disturbs the CP oscillations. Acoustic echoes are only detected in thick films with several hundred nanometers [21,40,43], while the thickest sample (23 L) here is still less than 15 nm.4. CONCLUSION
In conclusion, the interlayer lattice vibrations of few-layer generated by CPs were directly observed in the time domain. We found the coexistence of the LBM and SWM in such kind of group-10 TMDCs. The vibrational frequencies of the LBM were tightly dependent on the thickness, which can be utilized to characterize the number of layers of 2D materials beyond Raman spectroscopy. The IBFC per effective atom was determined to be , which was 2.5 times larger than that of graphene. In comparison with the ISFC, was demonstrated to have nearly isotropic interlayer coupling. In addition, the out-of-plane sound velocity was derived to be from the SWM. The results of interlayer interaction in layered can provide support for its application in nanomechanics like a high-frequency micro-mechanical resonator, surface cleaning, and driving motor.
APPENDIX A
The number of layers was determined by AFM. From the line profile across the step in Fig. 6, the films were , , , and , respectively.
The redshift absorption edges with the increasing number of layers can be seen in the Tauc plots in Fig. 7. The bandgaps of were extracted as 1.32 eV (2 L), 0.76 eV (5 L), 0.44 eV (8 L), 0.18 eV (10 L), and 0 eV (15 L, 17 L, and 23 L), which are plotted and marked by the squares in Fig. 7(i). The other fitting parameters of Eq. (1) are listed in Table 3.
Funding
National Natural Science Foundation of China (11874370, 61675217); Strategic Priority Research Program of Chinese Academy of Sciences (XDB16030700); Key Research Program of Frontier Science of Chinese Academy of Sciences (QYZDB-SSW-JSC041); Program of Shanghai Academic Research Leader (17XD1403900); Natural Science Foundation of Shanghai (18ZR1444700); Shanghai Rising-Star Program (A type 19QA1410000); Youth Innovation Promotion Association of the Chinese Academy of Sciences; High-End Foreign Expert Fellowship of the Ministry of Science and Technology of the P. R. China (G20190161002).
Disclosures
The authors declare that there are no conflicts of interest related to this paper.
REFERENCES
1. A. Ciarrocchi, A. Avsar, D. Ovchinnikov, and A. Kis, “Thickness-modulated metal-to-semiconductor transformation in a transition metal dichalcogenide,” Nat. Commun. 9, 919 (2018). [CrossRef]
2. Y. Wang, L. Li, W. Yao, S. Song, J. T. Sun, J. Pan, X. Ren, C. Li, E. Okunishi, Y.-Q. Wang, E. Wang, Y. Shao, Y. Y. Zhang, H. Yang, E. F. Schwier, H. Iwasawa, K. Shimada, M. Taniguchi, Z. Cheng, S. Zhou, S. Du, S. J. Pennycook, S. T. Pantelides, and H.-J. Gao, “Monolayer PtSe2, a new semiconducting transition-metal-dichalcogenide, epitaxially grown by direct selenization of Pt,” Nano Lett. 15, 4013–4018 (2015). [CrossRef]
3. M. Yan, E. Wang, X. Zhou, G. Zhang, H. Zhang, K. Zhang, W. Yao, N. Lu, S. Yang, S. Wu, T. Yoshikawa, K. Miyamoto, T. Okuda, Y. Wu, P. Yu, W. Duan, and S. Zhou, “High quality atomically thin PtSe2 films grown by molecular beam epitaxy,” 2D Mater. 4, 045015 (2017). [CrossRef]
4. Y. Zhao, J. Qiao, Z. Yu, P. Yu, K. Xu, S. P. Lau, W. Zhou, Z. Liu, X. Wang, W. Ji, and Y. Chai, “High-electron-mobility and air-stable 2D layered PtSe2 FETs,” Adv. Mater. 29, 1604230 (2017). [CrossRef]
5. K. Zhang, M. Feng, Y. Ren, F. Liu, X. Chen, J. Yang, X.-Q. Yan, F. Song, and J. Tian, “Q-switched and mode-locked Er-doped fiber laser using PtSe2 as a saturable absorber,” Photon. Res. 6, 893–899 (2018). [CrossRef]
6. L. Tao, X. Huang, J. He, Y. Lou, L. Zeng, Y. Li, H. Long, J. Li, L. Zhang, and Y. H. Tsang, “Vertically standing PtSe2 film: a saturable absorber for a passively mode-locked Nd:LuVO4 laser,” Photon. Res. 6, 750–755 (2018). [CrossRef]
7. M. Ghorbani-Asl, A. Kuc, P. Miró, and T. Heine, “A single-material logical junction based on 2D crystal PdS2,” Adv. Mater. 28, 853–856 (2016). [CrossRef]
8. H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators,” Nat. Phys. 9, 480–484 (2013). [CrossRef]
9. Z. Guo, S. Chen, Z. Wang, Z. Yang, F. Liu, Y. Xu, J. Wang, Y. Yi, H. Zhang, L. Liao, P. K. Chu, and X.-F. Yu, “Metal-ion-modified black phosphorus with enhanced stability and transistor performance,” Adv. Mater. 29, 1703811 (2017). [CrossRef]
10. Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X.-F. Yu, and P. K. Chu, “From black phosphorus to phosphorene: basic solvent exfoliation, evolution of Raman scattering, and applications to ultrafast photonics,” Adv. Func. Mater. 25, 6996–7002 (2015). [CrossRef]
11. A. Mokhtari and J. Chesnoy, “Resonant impulsive stimulated Raman scattering,” Europhys. Lett. 5, 523–528 (1988). [CrossRef]
12. Z. Huang, W. Zhang, and W. Zhang, “Computational search for two-dimensional MX2 semiconductors with possible high electron mobility at room temperature,” Materials 9, 716 (2016). [CrossRef]
13. W. Zhang, Z. Huang, W. Zhang, and Y. Li, “Two-dimensional semiconductors with possible high room temperature mobility,” Nano Res. 7, 1731–1737 (2014). [CrossRef]
14. H. Xu, H. Zhang, Y. Liu, S. Zhang, Y. Sun, Z. Guo, Y. Sheng, X. Wang, C. Luo, X. Wu, J. Wang, W. Hu, Z. Xu, Q. Sun, P. Zhou, J. Shi, Z. Sun, D. W. Zhang, and W. Bao, “Controlled doping of wafer-scale PtSe2 films for device application,” Adv. Funct. Mater. 29, 1805614 (2019). [CrossRef]
15. X. Yu, P. Yu, D. Wu, B. Singh, Q. Zeng, H. Lin, W. Zhou, J. Lin, K. Suenaga, Z. Liu, and Q. J. Wang, “Atomically thin noble metal dichalcogenide: a broadband mid-infrared semiconductor,” Nat. Commun. 9, 1545 (2018). [CrossRef]
16. M. O’Brien, N. McEvoy, C. Motta, J. Zheng, N. C. Berner, J. Kotakoski, K. Elibol, T. J. Pennycook, J. C. Meyer, C. Yim, M. Abid, T. Hallam, J. F. Donegan, S. Sanvito, and G. S. Duesberg, “Raman characterization of platinum diselenide thin films,” 2D Mater. 3, 021004 (2016). [CrossRef]
17. C. Yim, K. Lee, N. McEvoy, M. O’Brien, S. Riazimehr, N. C. Berner, C. P. Cullen, J. Kotakoski, J. C. Meyer, M. C. Lemme, and G. S. Duesberg, “High-performance hybrid electronic devices from layered PtSe2 films grown at low temperature,” ACS Nano 10, 9550–9558 (2016). [CrossRef]
18. S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9, 7142–7150 (2015). [CrossRef]
19. C. Klingshirn, Semiconductor Optics, 3rd ed. (Springer, 2007).
20. L. Wang, S. Zhang, N. McEvoy, Y. Sun, J. Huang, Y. Xie, N. Dong, X. Zhang, I. M. Kislyakov, J.-M. Nunzi, L. Zhang, and J. Wang, “Nonlinear optical signatures of the transition from semiconductor to semimetal in PtSe2,” Laser Photonics Rev. 13, 1900052 (2019). [CrossRef]
21. S. Ge, X. Liu, X. Qiao, Q. Wang, Z. Xu, J. Qiu, P.-H. Tan, J. Zhao, and D. Sun, “Coherent longitudinal acoustic phonon approaching THz frequency in multilayer molybdenum disulphide,” Sci. Rep. 4, 5722 (2014). [CrossRef]
22. H. Wang, C. Zhang, and F. Rana, “Ultrafast carrier dynamics in single and few atomic layer MoS2 studied by two-color optical pump-probe,” in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2013), paper QTu1D.2.
23. T. Mishina, K. Nitta, and Y. Masumoto, “Coherent lattice vibration of interlayer shearing mode of graphite,” Phys. Rev. B 62, 2908–2911 (2000). [CrossRef]
24. K. Ishioka, M. Hase, M. Kitajima, L. Wirtz, A. Rubio, and H. Petek, “Ultrafast electron-phonon decoupling in graphite,” Phys. Rev. B 77, 121402 (2008). [CrossRef]
25. F. Sun, Q. Wu, Y. L. Wu, H. Zhao, C. J. Yi, Y. C. Tian, H. W. Liu, Y. G. Shi, H. Ding, X. Dai, P. Richard, and J. Zhao, “Coherent helix vacancy phonon and its ultrafast dynamics waning in topological Dirac semimetal Cd3As2,” Phys. Rev. B 95, 235108 (2017). [CrossRef]
26. A. A. Melnikov, O. V. Misochko, and S. V. Chekalin, “Generation of coherent phonons in bismuth by ultrashort laser pulses in the visible and NIR: displacive versus impulsive excitation mechanism,” Phys. Lett. A 375, 2017–2022 (2011). [CrossRef]
27. O. V. Misochko, “Pump pulse duration dependence of coherent phonon amplitudes in antimony,” J. Exp. Theor. Phys. 123, 292–302 (2016). [CrossRef]
28. Z.-X. Hu, X. Kong, J. Qiao, B. Normand, and W. Ji, “Interlayer electronic hybridization leads to exceptional thickness-dependent vibrational properties in few-layer black phosphorus,” Nanoscale 8, 2740–2750 (2016). [CrossRef]
29. Y. Zhao, X. Luo, H. Li, J. Zhang, P. T. Araujo, C. K. Gan, J. Wu, H. Zhang, S. Y. Quek, M. S. Dresselhaus, and Q. Xiong, “Interlayer breathing and shear modes in few-trilayer MoS2 and WSe2,” Nano Lett. 13, 1007–1015 (2013). [CrossRef]
30. A. Kandemir, B. Akbali, Z. Kahraman, S. V. Badalov, M. Ozcan, F. Iyikanat, and H. Sahin, “Structural, electronic and phononic properties of PtSe2: from monolayer to bulk,” Semicond. Sci. Technol. 33, 085002 (2018). [CrossRef]
31. J.-B. Wu, Z.-X. Hu, X. Zhang, W.-P. Han, Y. Lu, W. Shi, X.-F. Qiao, M. Ijiäs, S. Milana, W. Ji, A. C. Ferrari, and P.-H. Tan, “Interface coupling in twisted multilayer graphene by resonant Raman spectroscopy of layer breathing modes,” ACS Nano 9, 7440–7449 (2015). [CrossRef]
32. Y. Zhao, J. Qiao, P. Yu, Z. Hu, Z. Lin, S. P. Lau, Z. Liu, W. Ji, and Y. Chai, “Extraordinarily strong interlayer interaction in 2D layered PtS2,” Adv. Mater. 28, 2399–2407 (2016). [CrossRef]
33. N. S. Luo, P. Ruggerone, and J. P. Toennies, “Theory of surface vibrations in epitaxial thin films,” Phys. Rev. B 54, 5051–5063 (1996). [CrossRef]
34. X. Miao, G. Zhang, F. Wang, H. Yan, and M. Ji, “Layer-dependent ultrafast carrier and coherent phonon dynamics in black phosphorus,” Nano Lett. 18, 3053–3059 (2018). [CrossRef]
35. X. Luo, X. Lu, G. K. W. Koon, A. H. C. Neto, B. Özyilmaz, Q. Xiong, and S. Y. Quek, “Large frequency change with thickness in interlayer breathing mode--significant interlayer interactions in few layer black phosphorus,” Nano Lett. 15, 3931–3938 (2015). [CrossRef]
36. X. Zhang, W. P. Han, J. B. Wu, S. Milana, Y. Lu, Q. Q. Li, A. C. Ferrari, and P. H. Tan, “Raman spectroscopy of shear and layer breathing modes in multilayer MoS2,” Phys. Rev. B 87, 115413 (2013). [CrossRef]
37. P. H. Tan, W. P. Han, W. J. Zhao, Z. H. Wu, K. Chang, H. Wang, Y. F. Wang, N. Bonini, N. Marzari, N. Pugno, G. Savini, A. Lombardo, and A. C. Ferrari, “The shear mode of multilayer graphene,” Nat. Mater. 11, 294–300 (2012). [CrossRef]
38. C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, and J. J. Hauser, “Coherent phonon generation and detection by picosecond light pulses,” Phys. Rev. Lett. 53, 989–992 (1984). [CrossRef]
39. W. Qian, H. Yan, J. J. Wang, Y. H. Zou, L. Lin, and J. L. Wu, “Observation of coherent phonons in silver nanoparticles embedded in BaO thin films,” Appl. Phys. Lett. 74, 1806–1808 (1999). [CrossRef]
40. C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34, 4129–4138 (1986). [CrossRef]
41. Al. A. Kolomenskii, H. A. Schuessler, V. G. Mikhalevich, and A. A. Maznev, “Interaction of laser-generated surface acoustic pulses with fine particles: surface cleaning and adhesion studies,” J. Appl. Phys. 84, 2404–2410 (1998). [CrossRef]
42. J. Lu, Q. Li, C.-W. Qiu, Y. Hong, P. Ghosh, and M. Qiu, “Nanoscale Lamb wave-driven motors in nonliquid environments,” Sci. Adv. 5, eaau8271 (2019). [CrossRef]
43. C. He, M. Daniel, M. Grossmann, O. Ristow, D. Brick, M. Schubert, M. Albrecht, and T. Dekorsy, “Dynamics of coherent acoustic phonons in thin films of CoSb3 and partially filled YbxCo4Sb12 skutterudites,” Phys. Rev. B 89, 174303 (2014). [CrossRef]