Abstract

Raman spectroscopy is a versatile tool widely used for comprehensive probing of crystal information. However, generally when applied in narrow-band-gap van der Waals crystals, it is liable to form a “bug,” especially in transition-metal-dichalcogenides (TMDs). That is, several resonant Raman-scattering (RS) modes will inevitably appear in the Raman spectra with strong intensity, interfering with the desired signal of optical-phonon modes. Here, we propose cross-sectional polarized Raman scattering capable of regulating the intensity of RS modes in accordance with quasi-sinusoidal rules. Typically, for MoS2 and WS2, when the polarization vector of excited light is along the c axis of the crystal, all RS modes are nearly completely “expunged” from the Raman spectra. The mechanism is that the absorption of most TMDs with a space group of R3m for the light polarized along the c axis is infinitesimal, thus forming a small coupling intensity of electronic states excited optically and acoustic-phonon modes at point M, which in turn restrain the appearance of RS modes. The regulating strategy proposed can be applied to other van der Waals crystals so as to obtain a high signal-to-noise ratio Raman spectrum.

© 2018 Chinese Laser Press

Corrections

Wei Zheng, Yanming Zhu, Fadi Li, and Feng Huang, "Raman spectroscopy regulation in van der Waals crystals: publisher’s note," Photon. Res. 6, 1101-1101 (2018)
http://proxy.osapublishing.org/prj/abstract.cfm?uri=prj-6-12-1101

17 October 2018: A correction was made to the author listing.

1. INTRODUCTION

Van der Waals crystals, such as layered semiconductor transition-metal-dichalcogenides (TMDs), are expected to integrate with silicon or other heterogeneous wafers as logic units to realize logical operations [13]. In order to fabricate an integrated logic device, the layered TMDs are inevitably bonded to other functional materials such as metal, organics, dielectrics, and semiconductors [46]. However, the bonding process may incite a potential problem: due to their small crystal lattice energy, van der Waals TMDs are liable to trigger crystal lattice distortion in the environment of a heterogeneous interface, thus resulting in some unpredictable optoelectronic properties and reducing the reliability of the TMD-based logic device [5,7]. Therefore, a non-destructive and in situ tool is needed to probe into the TMDs in the micro-zone and to provide accurate information about the changes in their lattice structure and optoelectronic properties.

Micro-Raman spectroscopy, meeting the above requirements, is an ideal tool for probing van der Waals crystals [810]. It has already been widely used to measure the crystallinity, number, and orientation of layers [11,12] and the types and quality of edges [13], as well as to analyze the perturbation effect under strain, doping, or electromagnetic conditions [8]. In spite of such extensive applications, Raman spectroscopy still has a “bug” for probing narrow-band-gap TMDs. Generally, a large number of resonant Raman-scattering (RS) modes, coming from the coupling of acoustic-phonon modes at point M and optically excited electronic states, occur in Raman spectra, which interfere optical-phonon (OP) modes under conventional excitation conditions (λexc=532,633 nm). This bug significantly decreases the signal-to-noise ratio (SNR) of Raman spectra in typical TMDs such as MoS2 and WS2 [9,1416].

As mentioned before, resonant Raman scattering in semiconductors mainly comes from the coupling of acoustic phonon modes and electronic states excited by photons. Thus, to eliminate the RS mode, it is necessary to inhibit the absorption of excited light in the measured crystals as much as possible. Here, typically for MoS2 and WS2, we first figure out the anisotropic absorption characteristics comprehensively within the visible light range via first-principles calculations. The results indicate that both MoS2 and WS2 have infinitesimal absorption for out-of-plane polarized light (eic axis), even if the excited photon energy exceeds the band gap. Based on theoretical understanding, we achieve a quasi-sinusoidal control of the scattering intensity in RS modes under the cross-sectional scattering geometry configuration, realize an almost complete suppression of the RS modes, and obtain Raman spectra with ultra-high SNR. The strategy used in this research of combining theory and experimental research can be also extended to the regulation and suppression of RS modes in other van der Waals crystals.

2. EXPERIMENTAL RESULTS AND DISCUSSION

The two typical van der Waals crystals for Raman regulation in this work, MoS2 and WS2, have an indirect bandgap of 1.5 eV and 1.4 eV, respectively [17,18]. In normal Raman-scattering measurements, usually, the excited laser wavelength is 532 nm and/or 633 nm, and with the wave vector ki along the c axis of crystals (i.e., kic axis, eic axis), any excited light polarized in-plane produces strong RS modes [8,14,15], as shown in Fig. 1. Obviously, the obtained typical Raman spectra contain a large number of RS modes, causing difficulties in identifying the lattice-distortion-sensitive OP modes [19,20], such as A1g.

 

Fig. 1. Typical Raman spectra of MoS2 and WS2 scattering from in-plane (eic axis). (a) Typical Raman-scattering spectrum of MoS2 excited by a 633 nm laser, and a large number of LA(M)-related RS modes are excited. All recoded modes in MoS2 Raman spectroscopy are identified as 179 [A1g(M)+LA(M)], 383 [E2g1(Γ)], 409 [A1g(Γ)], 421 [B2g2+E1u2(ΓA)], 454 [2LA(M)], 465 [A2u(Γ)], 529 [E1g(M)+LA(M)], 572 [2E1g(Γ)], 600 [E2g1(M)+LA(M)], 644 [A1g(M)+LA(M)], 767 (unknown), 785 (unknown), and 824 (unknown) cm1 [14,16]. (b) Typical Raman-scattering spectrum of WS2 excited by a 532 nm laser, and the recoded modes are identified as LA(M) at 175  cm1, E2g1(M)LA(M) at 195  cm1, A1g(M)LA(M) at 233  cm1, 2LA(M)2E2g2(M) at 298  cm1, E1g(M) at 323  cm1, 2LA(M) at 351  cm1, A1g(Γ) at 421  cm1,E2g1(M)+LA(M) at 523  cm1, A1g(M)+LA(M) at 585  cm1, and 4LA(M) at 701  cm1 [9].

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As mentioned earlier, the resonant Raman-scattering intensity is strongly dependent on the absorption of excited lights (absorption mainly comes from the electronic transitions). To understand the scattering behavior of RS modes in van der Waals crystals, it is necessary to probe into the anisotropic optical absorption characteristics systematically. Therefore, first we apply the first-principles method to calculate the absorption characteristics of MoS2 and WS2 to visible lights with different polarizations via the Perdew–Burke–Ernzerhof functional [21], and the results are shown in Fig. 2.

 

Fig. 2. Normalized optical absorption coefficients of the cross section (kia axis) in (a) MoS2 and (b) WS2 calculated via first principles, where ordinate θ is the angle between the incident light polarized vector ei and the c axis of the crystals. The absorption coefficients of the in-plane area (kic axis) in (c) MoS2 and (d) WS2, where the ordinate φ represents the angle between the incident light ei and the c axis.

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The results in Fig. 2 indicate that MoS2 and WS2 show no optical absorption anisotropy in-plane [Figs. 2(c) and 2(d)] yet boast strong anisotropy in the cross section [Figs. 2(a) and 2(b)]. Importantly, when the electric vector is along the c axis (eic axis, i.e., θ=0 or π), the absorption coefficient is close to zero, and it is also weakly related to photon energy, even for those whose energy is greater than the band gap.

The calculation results can be further clarified by a physical description as follows [22]. The electrons in the plane of layered MoS2 and WS2 can move freely and interaction with the photons’ polarization lies in-plane. For example, the conduction-band minimum (CBM) of layered WS2 is predominately constructed by W dz2 orbitals, whereas the valence-band maximum (VBM) constructed by W dxy and dx2y2 orbitals, leaves only a small amount of room for S px and py orbitals to contribute [23]. On the one hand, once the incident photon polarization lies in-plane along the a axis (corresponding to the x axis in mathematics), the absorption coefficient can be calculated by αa=|CBM|x|VBM|2=|dxdydzz2x2|2. The even integrand and the finite integral indicate that an oscillation between the W dz2 orbital and the S px orbital of electron density is induced by the photon polarized in-plane. Thereafter, it brings about a bright transition, absorbing the incident photons. On the other hand, if incident photon polarization is placed along the c axis (corresponding to the z axis in mathematics), the integrand will be odd, written as αc=|CBM|x|VBM|2=0, and the absorption coefficient will reach zero. From the above explanation, it is clear that optical absorption cannot be brought by photons polarized out-of-plane. MoS2, too, follows similar procedures.

These theoretical results give guidelines for designing a Raman-scattering geometric configuration to suppress RS modes. Based on the understanding of optical absorption in Fig. 2, we conduct Raman measurements on MoS2 and WS2 again under an x(z)x geometric configuration. The expected Raman spectra with a high SNR is obtained, and RS modes are nearly inhibited, as shown in Fig. 3. It is noteworthy that under such an out-of-plane polarization geometric configuration, unlike the increased intensity of A1g(Γ), the scattering intensity of E2g1(Γ) is weakened, regulated by the Raman selection rules.

 

Fig. 3. Improved Raman spectra of (a) MoS2 and (b) WS2 scattering from out-of-plane polarization (eic axis). Compared to Fig. 1, the RS modes here are fully suppressed and the high SNR of the OP mode is highlighted.

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To provide a clear explanation for the above satisfactory experimental results, it is necessary to conduct a systematic study of the evolution of RS modes when van der Waals MoS2 and WS2 are under different polarization conditions. In response, we carry out the following polarized Raman-scattering measurements comprehensively. Figures 4(a) and 4(b) show the cross-sectional angle-dependent polarized (CAP) Raman spectra, boasting strong anisotropy, while Figs. 4(c) and 4(d) show the in-plane angle-dependent polarized (IAP) Raman spectra, bearing almost no anisotropy.

 

Fig. 4. The cross-sectional angle-dependent polarized (CAP) Raman spectra of (a) MoS2 and (b) WS2, where the ordinate θ is defined as the angle between the incident light polarization ei and the c axis, and the in-plane angle-dependent polarized (IAP) Raman spectra of (c) MoS2 and (d) WS2, where the ordinate φ is defined as the angle between the incident light polarization ei and the a axis.

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It can be found through careful observation that OP and RS modes in Figs. 4(a) and 4(b) display distinct anisotropic behaviors. The relationship between the scattering intensity of the A1g OP mode and θ is close to the quasi-sine wave [details are shown in Figs. 5(a) and 5(b)], while the RS modes the quasi-cosine wave [Figs. 5(c) and 5(d)].

 

Fig. 5. Raman intensities of OP and RS modes extracted from Figs. 4(a) and 4(b) via Lorentzian fitting. (a) and (b) display angle-dependent intensities of A1g OP modes in MoS2 and WS2, respectively, and reveal a similar changing rule in MoS2 and WS2. The red line gives the corresponding fitting results based on the Raman selection rule, i.e., Eq. (1). (c) and (d) show the angle-dependent intensities of resonant scattering modes in layered MoS2 and WS2, respectively. All modes appear with the same θ angle dependence: when θ=(n+1/2)π, the scattering intensity reaches the highest value; while θ=nπ, the value approximates to zero.

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The anisotropic scattering behavior of the OP mode A1g accords with the Raman selection rule tightly, i.e., I|es·R·ei|2 [22,2427], where I is Raman-scattering intensity, ei is the polarization of incident light, es is the polarization of scattering light, and R is the Raman tensor. For the current measured crystals and geometric configuration, the Raman tensor is

R[A1g]=[aabeiϕ],
ei=es=(sinθ0cosθ).
Thus, the Raman-scattering intensity of the A1g mode is derived as follows:
IA1g(θ)|a|2sin4θ+|c|2cos4θ+12|a||c|sin2(2θ)cosϕ,
where ϕ is defined as the apparent phase [28]. The matched fitting results in Figs. 5(a) and 5(b) show that the formula can elaborate the anisotropic behaviors of A1g modes well.

However, Raman selection rules cannot describe the anisotropic behaviors of RS modes because they do not originate from the Raman-activated optical phonon. The RS modes are derived from the coupling intensity of optical excited electronic states and acoustic phonon modes at point M, so the light absorption coefficient can reasonably be used to explain the anisotropic behaviors of RS modes.

The scattering intensities of the RS modes in Figs. 5(c) and 5(d) completely reproduce anisotropic distribution of the optical absorption coefficients in Figs. 1(a) and 1(b). When the excited light polarization is perpendicular to the c axis of the crystals (i.e., θ=π/2 or 3π/2), the corresponding light absorption reaches the maximum value, which in turn makes the intensities of all the RS modes attain the maximum value. When the polarization is parallel to the c axis of the crystals (i.e., θ=0 or π), the light absorption attains the minimum value, resulting in the minimum RS mode intensities. Thus, the RS modes could be almost submerged in the background of Raman spectra, ensuring that the obtained Raman spectra have an ultra-high SNR. This strategy of Raman spectroscopy regulation can also be extended to other van der Waals crystals as an ideal tool for exploring and analyzing crystals’ quality and orientation, number of layers, types of edges, and effects of perturbations.

3. CONCLUSION

We propose a Raman regulation method or strategy to inhibit the occurrence of RS modes in the Raman spectra of van der Waals crystals and to obtain the desired Raman spectra with a high SNR. More specifically, when the polarization of excited light is along the c axis of crystals, the long-awaited improved Raman spectra containing only OP modes without any RS modes are achieved. The mechanism is that, under out-of-plane polarization, most TMDs with a space group of R3m will produce an extremely weak light absorption and, anomalously, an extremely strong Raman scattering of A1g OP modes.

4. METHODS

A. First-Principles Calculation

All density functional calculations are performed via the Vienna Ab-initio Simulation Package (VASP), using the Perdew–Burke–Ernzerhof functional [21]. The plane-wave energy cutoff for all the calculations is 680 eV. The lattice constants with a Monkhorst–Pack k-grid of 7×7×1 are not fully relaxed until the energy difference between two successive iterations is lower than 105  eV and the forces on every atom are lower than 103  eV/Å(1Å=0.1nm) [29]. GW calculations of optimized bulk structures are used to obtain electronic absorption spectra of linearly polarized light. The polarization absorption coefficient formula is written as α(θ)=αc+(αcαa)sin2θ [30], where αc is the absorption coefficient of the polarization vector parallel to the layers, while αa is that of the polarization vector perpendicular to the layers.

B. Raman-Scattering Measurements

MoS2 and WS2 samples are the ideal crystals for commercial use. CAP Raman measurements on MoS2 and WS2 are carried out via a Renishaw micro-Raman spectrometer (inVia Reflex) in backscattering geometry, using 633 nm and 532 nm lasers with a power of 0.25 mW and 0.3 mW, respectively. For CAP Raman-scattering measurement, the incident excitation laser focuses on the cross section of MoS2 (WS2), which is laid on a rotating stage by a 50× objective lens; the rotating angle θ is noted as the angle between the polarization vector ei of incident light and the c axis of the crystals. For IAP Raman-scattering measurement, the incident excitation laser focuses on the in-plane area of MoS2 (WS2); the rotating angle φ is noted as the angle between the polarization vector ei of the incident light and the a axis of the crystals. For the cross-sectional angle-dependent polarized Raman scattering, a polarizer was inserted into the scattering light path to enable the scattered light with polarization parallel to that of the incident laser, namely, eies.

Funding

National Natural Science Foundation of China (NSFC) (61427901, 61604178, 91333207, U1505252).

REFERENCES

1. F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014). [CrossRef]  

2. Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014). [CrossRef]  

3. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012). [CrossRef]  

4. W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018). [CrossRef]  

5. A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013). [CrossRef]  

6. W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016). [CrossRef]  

7. M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012). [CrossRef]  

8. X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015). [CrossRef]  

9. A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013). [CrossRef]  

10. A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013). [CrossRef]  

11. H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012). [CrossRef]  

12. A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006). [CrossRef]  

13. C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009). [CrossRef]  

14. K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014). [CrossRef]  

15. A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014). [CrossRef]  

16. G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999). [CrossRef]  

17. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010). [CrossRef]  

18. W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013). [CrossRef]  

19. A. C. Ferrari, “Raman spectroscopy of graphene and graphite: disorder, electron-phonon coupling, doping and nonadiabatic effects,” Solid State Commun. 143, 47–57 (2007). [CrossRef]  

20. L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011). [CrossRef]  

21. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996). [CrossRef]  

22. W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018). [CrossRef]  

23. J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013). [CrossRef]  

24. M. Cardona and G. Guntherodt, Light Scattering in Solids II (Springer, 1982).

25. W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015). [CrossRef]  

26. C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016). [CrossRef]  

27. C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016). [CrossRef]  

28. W. Zheng, J. Yan, F. Li, and F. Huang, “Elucidation of ‘phase difference’ in Raman tensor formalism,” Photon. Res. 6, 709–712 (2018). [CrossRef]  

29. H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976). [CrossRef]  

30. S. M. Heald and E. A. Stern, “Anisotropic X-ray absorption in layered compounds,” Phys. Rev. B 16, 5549–5559 (1977). [CrossRef]  

References

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  1. F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014).
    [Crossref]
  2. Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
    [Crossref]
  3. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
    [Crossref]
  4. W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
    [Crossref]
  5. A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
    [Crossref]
  6. W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
    [Crossref]
  7. M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
    [Crossref]
  8. X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
    [Crossref]
  9. A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
    [Crossref]
  10. A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
    [Crossref]
  11. H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
    [Crossref]
  12. A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
    [Crossref]
  13. C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
    [Crossref]
  14. K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
    [Crossref]
  15. A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
    [Crossref]
  16. G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999).
    [Crossref]
  17. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
    [Crossref]
  18. W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
    [Crossref]
  19. A. C. Ferrari, “Raman spectroscopy of graphene and graphite: disorder, electron-phonon coupling, doping and nonadiabatic effects,” Solid State Commun. 143, 47–57 (2007).
    [Crossref]
  20. L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
    [Crossref]
  21. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
    [Crossref]
  22. W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
    [Crossref]
  23. J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013).
    [Crossref]
  24. M. Cardona and G. Guntherodt, Light Scattering in Solids II (Springer, 1982).
  25. W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
    [Crossref]
  26. C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
    [Crossref]
  27. C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
    [Crossref]
  28. W. Zheng, J. Yan, F. Li, and F. Huang, “Elucidation of ‘phase difference’ in Raman tensor formalism,” Photon. Res. 6, 709–712 (2018).
    [Crossref]
  29. H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976).
    [Crossref]
  30. S. M. Heald and E. A. Stern, “Anisotropic X-ray absorption in layered compounds,” Phys. Rev. B 16, 5549–5559 (1977).
    [Crossref]

2018 (3)

W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
[Crossref]

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

W. Zheng, J. Yan, F. Li, and F. Huang, “Elucidation of ‘phase difference’ in Raman tensor formalism,” Photon. Res. 6, 709–712 (2018).
[Crossref]

2016 (3)

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
[Crossref]

2015 (2)

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
[Crossref]

2014 (4)

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014).
[Crossref]

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
[Crossref]

2013 (5)

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
[Crossref]

J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013).
[Crossref]

2012 (3)

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

2011 (1)

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

2010 (1)

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

2009 (1)

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

2007 (1)

A. C. Ferrari, “Raman spectroscopy of graphene and graphite: disorder, electron-phonon coupling, doping and nonadiabatic effects,” Solid State Commun. 143, 47–57 (2007).
[Crossref]

2006 (1)

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

1999 (1)

G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999).
[Crossref]

1996 (1)

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[Crossref]

1977 (1)

S. M. Heald and E. A. Stern, “Anisotropic X-ray absorption in layered compounds,” Phys. Rev. B 16, 5549–5559 (1977).
[Crossref]

1976 (1)

H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976).
[Crossref]

Achete, C. A.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Ajayan, P. M.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Anghel, S.

A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
[Crossref]

Babinski, A.

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

Baillargeat, D.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Basko, D. M.

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
[Crossref]

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Berkdemir, A.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Botello-Méndez, A. R.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Brown, L.

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

Burke, K.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[Crossref]

Cancado, L. G.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Capaz, R. B.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Cardona, M.

M. Cardona and G. Guntherodt, Light Scattering in Solids II (Springer, 1982).

Casiraghi, C.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Charlier, J.-C.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Chia, C.-I.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Chu, L.

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

Coleman, J. N.

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

Crespi, V. H.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Deligeorgis, G.

A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
[Crossref]

Dresselhaus, G.

G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999).
[Crossref]

Dresselhaus, M. S.

G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999).
[Crossref]

Dubey, M.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014).
[Crossref]

Eda, G.

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

Edwin, T. H. T.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Elías, A. L.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Ernzerhof, M.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[Crossref]

Fasoli, A.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Faugeras, C.

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

Ferrari, A. C.

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
[Crossref]

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

A. C. Ferrari, “Raman spectroscopy of graphene and graphite: disorder, electron-phonon coupling, doping and nonadiabatic effects,” Solid State Commun. 143, 47–57 (2007).
[Crossref]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Frey, G. L.

G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999).
[Crossref]

Geim, A. K.

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Georgi, C.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Ghorannevis, Z.

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

Golasa, K.

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

Gong, Y.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Grigorieva, I. V.

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

Grundmann, M.

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

Grzeszczyk, M.

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

Guntherodt, G.

M. Cardona and G. Guntherodt, Light Scattering in Solids II (Springer, 1982).

Gutiérrez, H. R.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Hartschuh, A.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Havener, R. W.

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

He, J.

W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
[Crossref]

Heald, S. M.

S. M. Heald and E. A. Stern, “Anisotropic X-ray absorption in layered compounds,” Phys. Rev. B 16, 5549–5559 (1977).
[Crossref]

Heinz, T. F.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Hone, J.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Huang, F.

W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
[Crossref]

W. Zheng, J. Yan, F. Li, and F. Huang, “Elucidation of ‘phase difference’ in Raman tensor formalism,” Photon. Res. 6, 709–712 (2018).
[Crossref]

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
[Crossref]

W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
[Crossref]

Huang, P. Y.

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

Ji, X.

W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
[Crossref]

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Jiang, D.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Jiang, D.-S.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Jorio, A.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Kalantar-Zadeh, K.

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

Kang, J.

J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013).
[Crossref]

Kim, C.-J.

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

Kis, A.

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

Kloc, C.

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

Kranert, C.

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

Kulmala, T. S.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Kulyuk, L.

A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
[Crossref]

Lazzeri, M.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Lee, C.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Lei, S.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Leszczynski, P.

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

Levendorf, M. P.

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

Li, F.

Li, G.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Li, H.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Li, J.

J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013).
[Crossref]

Liang, Y.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Lin, J.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Lin, R.

W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
[Crossref]

W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
[Crossref]

Lin, Z.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Liu, Z.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Lombardo, A.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

López-Urías, F.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Lou, J.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Mak, K. F.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Martins Ferreira, E. H.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Matthews, M. J.

G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999).
[Crossref]

Maude, D. K.

A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
[Crossref]

Mauri, F.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Meyer, J. C.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Mitioglu, A. A.

A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
[Crossref]

Monkhorst, H. J.

H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976).
[Crossref]

Moutinho, M. V. O.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Muller, D. A.

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

Nicolet, A. A. L.

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

Novoselov, K. S.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Olivier, A.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Pack, J. D.

H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976).
[Crossref]

Pantelides, S. T.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Park, J.

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

Perdew, J. P.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[Crossref]

Perea-López, N.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Piscanec, S.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Plochocka, P.

A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
[Crossref]

Potemski, M.

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

Qian, H.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Qiao, X.-F.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Ramasubramaniam, A.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014).
[Crossref]

Ran, J.

W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
[Crossref]

Roth, S.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Scardaci, V.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

Schmidt-Grund, R.

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

Shan, J.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Shi, G.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Shi, W.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Stavale, F.

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Stern, E. A.

S. M. Heald and E. A. Stern, “Anisotropic X-ray absorption in layered compounds,” Phys. Rev. B 16, 5549–5559 (1977).
[Crossref]

Strano, M. S.

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

Sturm, C.

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

Tan, P.-H.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

Tay, B. K.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Tenne, R.

G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999).
[Crossref]

Terrones, H.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Terrones, M.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Toh, M.

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

Tongay, S.

J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013).
[Crossref]

Vajtai, R.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Wang, B.

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Wang, H.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014).
[Crossref]

Wang, Q. H.

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

Wang, X.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Wu, H.

Wu, J.

J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013).
[Crossref]

Wu, J.-B.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Wysmolek, A.

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

Xia, F.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014).
[Crossref]

Xiao, D.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014).
[Crossref]

Xu, K.

W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
[Crossref]

Yakobson, B. I.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Yan, J.

Yang, F.

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Yap, C. C. R.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Ye, G.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Zhang, Q.

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Zhang, X.

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Zhang, Z.

W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
[Crossref]

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
[Crossref]

Zhao, W.

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

Zheng, R.

Zheng, W.

W. Zheng, J. Yan, F. Li, and F. Huang, “Elucidation of ‘phase difference’ in Raman tensor formalism,” Photon. Res. 6, 709–712 (2018).
[Crossref]

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
[Crossref]

W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
[Crossref]

W. Zheng, R. Zheng, F. Huang, H. Wu, and F. Li, “Raman tensor of AlN bulk single crystal,” Photon. Res. 3, 38–43 (2015).
[Crossref]

Zhou, J.

J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013).
[Crossref]

Zhou, W.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Zou, X.

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

ACS Nano (3)

W. Zheng, R. Lin, J. Ran, Z. Zhang, X. Ji, and F. Huang, “Vacuum-ultraviolet photovoltaic detector,” ACS Nano 12, 425–431 (2018).
[Crossref]

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.-H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

W. Zheng, F. Li, G. Li, Y. Liang, X. Ji, F. Yang, Z. Zhang, and F. Huang, “Laser tuning in van der Waals crystals,” ACS Nano 12, 2001–2007 (2018).
[Crossref]

Adv. Electron. Mater. (1)

W. Zheng, Z. Zhang, R. Lin, K. Xu, J. He, and F. Huang, “High-crystalline 2D layered PbI2 with ultrasmooth surface: liquid-phase synthesis and application of high-speed photon detection,” Adv. Electron. Mater. 2, 1600291 (2016).
[Crossref]

Adv. Funct. Mater. (1)

H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385–1390 (2012).
[Crossref]

Appl. Phys. Lett. (2)

K. Gołasa, M. Grzeszczyk, P. Leszczyński, C. Faugeras, A. A. L. Nicolet, A. Wysmołek, M. Potemski, and A. Babiński, “Multiphonon resonant Raman scattering in MoS2,” Appl. Phys. Lett. 104, 092106 (2014).
[Crossref]

J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, “Band offsets and heterostructures of two-dimensional semiconductors,” Appl. Phys. Lett. 102, 012111 (2013).
[Crossref]

Chem. Soc. Rev. (1)

X. Zhang, X.-F. Qiao, W. Shi, J.-B. Wu, D.-S. Jiang, and P.-H. Tan, “Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material,” Chem. Soc. Rev. 44, 2757–2785 (2015).
[Crossref]

Nano Lett. (2)

L. G. Cancado, A. Jorio, E. H. Martins Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Nat. Mater. (1)

Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. K. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135–1142 (2014).
[Crossref]

Nat. Nanotechnol. (2)

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
[Crossref]

Nat. Photonics (1)

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8, 899–907 (2014).
[Crossref]

Nature (2)

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

M. P. Levendorf, C.-J. Kim, L. Brown, P. Y. Huang, R. W. Havener, D. A. Muller, and J. Park, “Graphene and boron nitride lateral heterostructures for atomically thin circuitry,” Nature 488, 627–632 (2012).
[Crossref]

Photon. Res. (2)

Phys. Rev. B (4)

H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Phys. Rev. B 13, 5188–5192 (1976).
[Crossref]

S. M. Heald and E. A. Stern, “Anisotropic X-ray absorption in layered compounds,” Phys. Rev. B 16, 5549–5559 (1977).
[Crossref]

A. A. Mitioglu, P. Plochocka, G. Deligeorgis, S. Anghel, L. Kulyuk, and D. K. Maude, “Second-order resonant Raman scattering in single-layer tungsten disulfide WS2,” Phys. Rev. B 89, 245442 (2014).
[Crossref]

G. L. Frey, R. Tenne, M. J. Matthews, M. S. Dresselhaus, and G. Dresselhaus, “Raman and resonance Raman investigation of MoS2 nanoparticles,” Phys. Rev. B 60, 2883–2892 (1999).
[Crossref]

Phys. Rev. Lett. (4)

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
[Crossref]

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor formalism for optically anisotropic crystals,” Phys. Rev. Lett. 116, 127401 (2016).
[Crossref]

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[Crossref]

Sci. Rep. (2)

C. Kranert, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “Raman tensor elements of β-Ga2O3,” Sci. Rep. 6, 35964 (2016).
[Crossref]

A. Berkdemir, H. R. Gutiérrez, A. R. Botello-Méndez, N. Perea-López, A. L. Elías, C.-I. Chia, B. Wang, V. H. Crespi, F. López-Urías, J.-C. Charlier, H. Terrones, and M. Terrones, “Identification of individual and few layers of WS2 using Raman spectroscopy,” Sci. Rep. 3, 1755 (2013).
[Crossref]

Solid State Commun. (1)

A. C. Ferrari, “Raman spectroscopy of graphene and graphite: disorder, electron-phonon coupling, doping and nonadiabatic effects,” Solid State Commun. 143, 47–57 (2007).
[Crossref]

Other (1)

M. Cardona and G. Guntherodt, Light Scattering in Solids II (Springer, 1982).

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Figures (5)

Fig. 1.
Fig. 1. Typical Raman spectra of MoS 2 and WS 2 scattering from in-plane ( e i c axis). (a) Typical Raman-scattering spectrum of MoS 2 excited by a 633 nm laser, and a large number of LA(M)-related RS modes are excited. All recoded modes in MoS 2 Raman spectroscopy are identified as 179 [ A 1 g ( M ) + LA ( M ) ] , 383 [ E 2 g 1 ( Γ ) ] , 409 [ A 1 g ( Γ ) ] , 421 [ B 2 g 2 + E 1 u 2 ( Γ A ) ] , 454 [2LA(M)], 465 [ A 2 u ( Γ ) ] , 529 [ E 1 g ( M ) + LA ( M ) ] , 572 [ 2 E 1 g ( Γ ) ] , 600 [ E 2 g 1 ( M ) + LA ( M ) ] , 644 [ A 1 g ( M ) + LA ( M ) ] , 767 (unknown), 785 (unknown), and 824 (unknown) cm 1 [14,16]. (b) Typical Raman-scattering spectrum of WS 2 excited by a 532 nm laser, and the recoded modes are identified as LA(M) at 175    cm 1 , E 2 g 1 ( M ) LA ( M ) at 195    cm 1 , A 1 g ( M ) LA ( M ) at 233    cm 1 , 2 LA ( M ) 2 E 2 g 2 ( M ) at 298    cm 1 , E 1 g ( M ) at 323    cm 1 , 2LA(M) at 351    cm 1 , A 1 g ( Γ ) at 421    cm 1 , E 2 g 1 ( M ) + LA ( M ) at 523    cm 1 , A 1 g ( M ) + LA ( M ) at 585    cm 1 , and 4LA(M) at 701    cm 1 [9].
Fig. 2.
Fig. 2. Normalized optical absorption coefficients of the cross section ( k i a axis) in (a)  MoS 2 and (b)  WS 2 calculated via first principles, where ordinate θ is the angle between the incident light polarized vector e i and the c axis of the crystals. The absorption coefficients of the in-plane area ( k i c axis) in (c)  MoS 2 and (d)  WS 2 , where the ordinate φ represents the angle between the incident light e i and the c axis.
Fig. 3.
Fig. 3. Improved Raman spectra of (a)  MoS 2 and (b)  WS 2 scattering from out-of-plane polarization ( e i c axis). Compared to Fig. 1, the RS modes here are fully suppressed and the high SNR of the OP mode is highlighted.
Fig. 4.
Fig. 4. The cross-sectional angle-dependent polarized (CAP) Raman spectra of (a)  MoS 2 and (b)  WS 2 , where the ordinate θ is defined as the angle between the incident light polarization e i and the c axis, and the in-plane angle-dependent polarized (IAP) Raman spectra of (c)  MoS 2 and (d)  WS 2 , where the ordinate φ is defined as the angle between the incident light polarization e i and the a axis.
Fig. 5.
Fig. 5. Raman intensities of OP and RS modes extracted from Figs. 4(a) and 4(b) via Lorentzian fitting. (a) and (b) display angle-dependent intensities of A 1 g OP modes in MoS 2 and WS 2 , respectively, and reveal a similar changing rule in MoS 2 and WS 2 . The red line gives the corresponding fitting results based on the Raman selection rule, i.e., Eq. (1). (c) and (d) show the angle-dependent intensities of resonant scattering modes in layered MoS 2 and WS 2 , respectively. All modes appear with the same θ angle dependence: when θ = ( n + 1 / 2 ) π , the scattering intensity reaches the highest value; while θ = n π , the value approximates to zero.

Equations (3)

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R [ A 1 g ] = [ a a b e i ϕ ] ,
e i = e s = ( sin θ 0 cos θ ) .
I A 1 g ( θ ) | a | 2 sin 4 θ + | c | 2 cos 4 θ + 1 2 | a | | c | sin 2 ( 2 θ ) cos ϕ ,

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