Abstract
Using the classical molecular dynamics simulations, we have investigated the thermally-excited ripples of the AA- and AB-stacking bilayer graphenes (BLGs) at different temperatures, and compared them with those of the single layer graphene (SLG). It is found that: (1) the ripples in both AA- and AB-stacking BLGs are intrinsic with a characteristic size of about 100 Å at room temperature, increasing with increase of temperature. (2) The ripple’s intralayer height-height correlation functions for the two types of BLGs follow a power-law behavior, G h (q) ~ q -α, with the same scaling exponent at the same temperature, which decreases as temperature increases. (3) The ripple’s height of the AB-stacking BLG is larger than that of the AA-stacking one at the lower temperatures. (4) Finally, the ripple’s height in the two types of BLGs is greatly smaller than that in the SLG, which is consistent with the experimental results.
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S.V. Morozov, K.S. Novoselov, M.I. Katsnelson, F. Schedin, L.A. Ponomarenko, D. Jiang, A.K. Geim, Phys. Rev. Lett. 97, 016801 (2006)
A.K. Geim, K.S. Novoselov, Nature Mater. 6, 183 (2007)
K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)
K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature (London) 438, 197 (2005)
Y.B. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature (London) 438, 201 (2005)
J.S. Bunch, Y. Yaish, M. Brink, K. Bolotin, P.L. McEuen, Nano. Lett. 5, 287 (2005)
C. Berger, Z. Song, T. Li, X. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, W.A. de Heer, J. Phys. Chem. B 108, 19912 (2004)
Z. Liu, K. Suenaga, P.J.F. Harris, S. Iijima, Phys. Rev. Lett. 102, 015501 (2009)
C.L. Lu, C.P. Chang, M.F. Lin, Eur. Phys. J. B 60, 161 (2007)
J.H. Ho, C.L. Lu, C.C. Hwang, C.P. Chang, M.F. Lin, Phys. Rev. B 74, 085406 (2006)
P.L. de Andres, R. Ramírez, J.A. Vergés, Phys. Rev. B 77, 045403 (2008)
R.E. Peierls, Helv. Phys. Acta 7, 81 (1934)
R.E. Peierls, Ann. Inst. Henri Poincare 5, 177 (1935)
L.D. Landau, Phys. Z. Sowjetunion 11, 26 (1937)
L.D. Landau, E.M. Lifshitz, in Statistical Physics, Part I (Pergamon, Oxford, 1980), Sects. 137, 138
M. Zinke-Allmang, L.C. Feldman, M.H. Grabow, Surf. Sci. Rep. 16, 377 (1992)
J.W. Evans, P.A. Thiel, M.C. Bartelt, Surf. Sci. Rep. 61, 1 (2006)
D.R. Nelson, L. Peliti, J. Phys. 48, 1085 (1987)
P. Le Doussal, L. Radzihovsky, Phys. Rev. Lett. 69, 1209 (1992)
J.C. Meyer, A.K. Geim, M.I. Katsnelson, K.S. Novoselov, T.J. Booth, S. Roth, Nature (London) 446, 60 (2007)
A. Fasolino, J.H. Los, M.I. Katsnelson, Nature Mater. 6, 858 (2007)
M.I. Katsnelson, A.K. Geim, Phil. Trans. R. Soc. A 366, 195 (2008)
K.V. Zakharchenko, M.I. Katsnelson, A. Fasolino, Phys. Rev. Lett. 102, 046808 (2009)
F. Schedin, A.K. Geim, S.V. Morozov, E.W. Hill, P. Blake, M.I. Katsnelson, K.S. Novoselov, Nature Mater. 6, 652 (2007)
J.M. Carlsson, Nature Mater. 6, 801 (2007)
J.C. Meyer, A.K. Geim, M.I. Katsnelson, K.S. Novoselov, D. Obergfell, S. Roth, C. Girit, A. Zettl, Solid State Commun. 143, 101 (2007)
W.G. Hoover, Phys. Rev. A 31, 1695 (1985)
J. Tersoff, Phys. Rev. B 37, 6991 (1988)
V.N. Popov, L. Henrard, Phys. Rev. B 65, 235415 (2002)
J.P. Lu, W. Yang, Phys. Rev. B 49, 11421 (1994)
D.C. Liu, J. Nocedal, Math. Program. B 45, 503 (1989)
D.R. Nelson, in Statistical Mechanics of Membranes and Surfaces, edited by D. Nelson, T. Piran, S. Weinberg, 2nd edn. (World Scientific, Singapore, 2004)
J.H. Los, M.I. Katsnelson, O.V. Yazyev, K.V. Zakharchenko, A. Fasolinol, Phys. Rev. B 80, 121405 (2009)
K.V. Zakharchenko, J.H. Los, M.I. Katsnelson, A. Fasolino, arXiv:1004.0126
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Chang, X., Ge, Y. & Dong, J. Ripples of AA and AB stacking bilayer graphenes. Eur. Phys. J. B 78, 103–109 (2010). https://doi.org/10.1140/epjb/e2010-10498-8
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DOI: https://doi.org/10.1140/epjb/e2010-10498-8