1. A. K. Geim, and K. S. Novoselov: Nat. Mater. 6, 183 (2007).
2.
A. K. Geim, K. S. Novoselov, S.V. Morozov, D. Jiang, S. V. Dubonos, I. V. Grigorieva,
and A. A. Firsov: Science 306, 666 (2004).
3.
K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer, U. Zeitler, J. C. Maan,
G. S. Boebinger, P. Kim, and A. K. Geim: Science 315, 1379 (2007).
4. J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth:
Nature 446, 60 (2007).
5. 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: Phys. Rev. Lett. 97, 187401 (2006).
6. A. C. Ferrari: Sol. Stat. Commun. 143, 47-57 (2007).
7. D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz: Nano
Lett. 7, 238-242 (2007).
8. D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz: Sol.
Stat. Commun. 143, 44-46 (2007).
9. A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S.
Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood: Nat.
Nanotechnol. 3, 210-215 (2008).
10. Z. Ni, Y. Wang, T. Yu Z. Shen: Nano Res. 1, 273-291 (2008).
11. H. Wang, Y. Wang, X. Cao, M. Feng, G. Lan: J. Raman Spectrosc. 40, 1791-1796 (2009).
12. R. W. Havener, H. Zhuang, L. Brown, R. G. Hennig, and J. Park: Nano Lett. 12, 3162
(2012).
13. Y. Y. Wang, Z. H. Ni, and Z. X. Shen: Appl. Phys. Lett. 92, 043121 (2008).
14. A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C.
Cairaghi: Nano Lett. 12, 3925-3930 (2012).
15. C. Stampfer, F. Molitor, D. Graf, and K. Ensslin: Appl. Phys. Lett. 91, 241907 (2007).
16. J. Yan, Y. Zhang, P. Kim, and A. Pinczuk: Phys. Rev. Lett. 98, 166802 (2007).
17. U. Fano: Phys. Rev. 124, 1866-1878 (1961).
18. F. Cerdeira, T.A. Fjeldly, and M. Cardona: Phys. Rev. B 8, 4734 (1973).
19. M.V. Klein, in Light scattering in solids I, Topics in applied physics (Springer-Verlag,
Berlin, 1983) Vol. 8, pp. 147-204.
20. P. H. Tan, W. P. Han, W. J. Zhao, Z. H. Wu, K. Chang, H. Wang, Y. F. Wang, N. Bonini,
N. Marzari, G. Savini, A. Lombardo, and A. C. Ferrari: Nature Mat. 11, 294-300 (2014).
21. E. H. Hasedo, A. R. T. Nugraha, M. S. Dresselhaus and R. Saito: Phys. Rev. B 90, 245140
(2014).
22. P. C. Eklund and K. R. Subbaswamy: Phys. Rev. B 20, 5157 (1979).
23. S. D. M. Brown, A. Jorio, P. Corio, M. S. Dresselhaus, G. Dresselhaus, R. Saito, and K.
Kneipp: Phys. Rev. B 63, 155414 (2001).
24. C. Jiang, K. Kempa, J. Zhao, U. Schlecht, U. Kolb, T. Basche, M. Burghard, and A.
Mews: Phys. Rev. B 66, 161404 (2002).
25. D. Yoon, D. Jeong, H.-J. Lee, R. Saito, Y.-W. Son, H.-C. Li, and H. Cheong: Carbon 61,
373 (2013).
26. A. B. Kuzmenko, L. Benfatto, E. Cappelluti, I Crassee, D. van der Marel, P. Blake, K. S.
Novoselov, and A. K. Geim: Phys. Rev. Lett. 103, 116804 (2009).
27. J. M. Baranowski, M. Mozdzonek, P. Dabrowski, K. Grodecki, P. Osewski, W.
Kozlowski, M. Kopciuszynski, and W. Strupinski: Graphene 2, 115-120 (2013).
28. R. Kitaura, Y. Miyata, R. Xiang, J. Hone, J. Kong, R. S. Ruoff, and S. Maruyama: J.
Phys. Soc. Jpn. 84, 121013 (2015).
29. X. Chen, P. Zhao, R. Xiang, S. Kim, J.-H. Cha, S. Chiashi, S. Maruyama: Carbon 94,
810 (2015).
30. P. Zhao, S. Kim, X. Chen, E. Einarsson, M. Wang, Y. Song, H. Wang, S. Chiashi, R.
Xiang, and S. Maruyama: ACS Nano 8, 11631 (2014).
31. W. Zhang, J. Yan, C.-H. Chen, L. Lei, J.-L Kuo, Z. Shen, and L.-J. Li: Nat. Commun. 4,
2074 (2013).
32. J.-B. Wu, M.-L. Lin, X. Cong, H.-N. Liu, and P.-H. Tan: Chem. Soc. Rev. 47, 1822
(2018).
33. Y. Chen, and L. Dai: Appl. Opt. 55, 4085 (2016).
34. L. M. Malard, J. Nilsson, D. C. Elias, J. C. Brant, F. Plentz, E. S. Alves, A. H. Castro
Neto, and M. A. Pimenta: Phys. Rev. B 76, 201401 (2007).
35. M. Hase, M. Kitajima, S. Nakashima, and K. Mizoguchi: Phys. Rev. Lett. 88, 067401
(2002).
36. O.V. Misochko, K. Ishioka, M. Hase, and M. Kitajima: J. Phys.: Condens. Mater. 19,
156227 (2007).
37. D. Huehn, A. Govolov, P. R. Gil, and W. J. Parak: Adv. Funct. Mater. 22, 294 (2012).
38. M. Sparks: J. Appl. Phys. 47, 837 (1976).
39. C. Ott, A. Kadum, P. Raith, K. Meyer, M. Laux, J. Evers, C. H. Keitel, C. H. Greene, and
T. Pfeifer: Science 340, 716 (2013).
40. K. Kato, Y. Hasegawa, K. Oguri, T. Tawara, T. Nishikawa, and H. Gotoh: Phys. Rev. B
97, 104301 (2018).
41. S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A.
Knorr, M. Spinkle, C. Berger, W. A. de Heer, H. Schneider, and M. Helm: Phys. Rev.
Lett. 107, 237401 (2011).
42. N. W. Ashcroft and N. Mermin, Solid State Physics (Cengage Learning Inc., 1976) Chap.
2.
43. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim: Rev.
Mod. Phys. 81, 109 (2009).
44. I. Katayama, K. Inoue, Y. Arashida, Y. Wu, H. Yang, T. Inoue, S. Chiashi, S. Maruyama,
T. Nagao, M. Kitajima, and J. Takeda: Phys. Rev. B 101, 245408 (2020).
Figure captions
Figure 1: Sample of the graphene stack and Raman maps. (a) Raman spectrum of monolayer
graphene. The inset is an optical microscope image of the graphene multilayer stack. The
area indicated by a red rectangle was examined by Raman mapping. (b) Raman intensity
maps of the G peak, (c) Si optical phonon band, and (d) 2D peak. The hexagonal shape of
graphene layers is also observed in Raman images. (e) Layer number dependence of the Gpeak intensity. The G-band intensity is reported to increase almost linearly with layer number
for sheets that are less than ~10 layers and then decrease for thicker graphene sheets [10,13].
The observed dependence is similar to the trend for thinner sheets.
Figure 2: Raman maps of (a) intensity IG, (b) frequency fG, (c) damping constant G, and
(d) electron–phonon coupling strength |1/q| for the G-band around the 1–2-ML border of
the graphene stack. The data were obtained at a laser power of 0.23 mW. The values of fG,
G, and |1/q| were obtained using BWF fittings at each scanning point. The maps clearly
indicate the change in |1/q|, as well fG and G, along the border.
Figure 3: Line shapes of the G peaks. (a) Raman spectra (filled circles), fits by the BWF
formula (dashed lines), and fits by the BWF–Gauss function (solid lines). The data for 1and 2-ML graphene and graphite are plotted. (b) Changes in line shapes owing to slight
changes in 1/q values in the BWF–Gauss function. The plot ensures that 1/q values are
clearly determined by the fitting. (c) Layer number dependence of the center frequency (fG)
and 1/q obtained by the BWF–Gauss fitting. The Raman spectra were obtained at a power
of 0.23 mW. For the fitting, we used the spectra integrated over scanned positions on areas
at each layer without defects. Error bars in the figure are estimated from the fitting accuracy
of the parameter q.
Figure 4: Laser-power dependence of 1/q for 1, 2, and 3 ML of the graphene stack. The result
for HOPG is also illustrated for comparison. The value of 1/q monotonously decreases with
laser power, except for 1 ML. Dashed lines are guidelines for the experimental data points.
The |1/q| images for the 1–2-ML border measured at 10- and 20-mW laser powers are
presented on the right-hand side. The circle indicates discrepancy from the monotonic
decrease in 1/q for the 1-ML sample.
Figure 5: (a) Comparison of the observation and calculations for the laser-power
dependence of 1/q for monolayer graphene. Circle: experiments; blue dotted line:
extrapolation for temperature from the temperature dependence in reference [40]; red
dashed line: calculated curve obtained by taking into account the laser-heating-induced
Fermi energy change. (b) Relation of 1/q vs. the phase between discrete phonons and the
electronic continuum calculated using Eq. 2) [39]. In this figure, the observed values are
plotted in green circles, together with the values of Si for comparison (blue triangles) [40].
(c) Laser-power dependence of calculated 1/q for monolayer graphene with different initial
Fermi energies |𝐸0𝐹 | without laser excitation. Brown dotted line: |𝐸0𝐹 | = 0.10 eV, pink dashtwo-dot line:|𝐸0𝐹 | = 0.15 eV, red solid line:|𝐸0𝐹 | = 0.20 eV (this is the same as that of our
sample), blue dash-dot line:|𝐸0𝐹 | = 0.25 eV, green dotted line: |𝐸0𝐹| = 0.30 eV. We have also
calculated the values for |𝐸 | = 0, which results in the same curve as that for |𝐸 | =
0.15 eV.
Fig. 1 Kitajima et al.
Fig. 2 Kitajima et al.
Fig. 3 Kitajima et al.
Fig. 4 Kitajima et al.
Fig. 5 Kitajima et al.
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