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In our daily life, frictions are very common when two bodies in direct contact relatively move. However, when two bodies are separated by a finite distance, due to the quantum fluctuations inside the bodies, they may still experience a friction when they relatively move. Such a phenomenon is often called quantum friction, which has been studied for more than a decade. It has shown in previous studies that the surface modes, such as surface phonon polaritions (SPhPs) or surface plasmon polaritions (SPPs) have significant contribution to enhancing the quantum friction. However, to the best of our knowledge, the contribution of coupling from SPhPs and SPPs to quantum friction is still unknown. Here, we report a detailed study on the quantum frictions between two graphene sheets with the silicon carbide (SiC) substrates. For comparison, the quantum frictions between two other samples, i.e., SiC/SiC and graphene/graphene are also studied. As indicated in previous studies, SPhPs and SPPs, supported by SiC and graphene, respectively, can couple together in special frequency ranges. The coupling of SPhPs and SPPs can be tuned by varying the chemical potential of graphene. The coupling modes shift toward higher frequency as the chemical potential increases. Firstly, we analyze qualitatively the effects of coupled surface modes on quantum friction with the help of dispersion relation. Secondly, we calculate the quantum friction coefficients numerically for the three different samples. We find that due to the coupling of SPhPs and SPPs, the quantum friction between graphene sheets with SiC substrates is larger than that between the SiC or monolayer graphene sheets. We demonstrate that the coupling of SPhPs and SPPs can be modulated by chemical potential of graphene; therefore, the relationship between quantum friction coefficient and chemical potential is also studied. We observe that with the increase of chemical potential, quantum friction coefficient follows a non-monotonic trend, i.e., it first increases to its maximum value then decreases. We believe that our studies are not only helpful in understanding the micro mechanisms of friction, but also meaningful in the fabrications of micro- and nano-electromechanical systems.
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Keywords:
- quantum friction /
- graphene /
- plasmons
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[1] Dorofeyev I, Fuchs H, Wenning G, Gotsmann B 1999 Phys. Rev. Lett. 83 2402
[2] Stipe B C, Mamin H J, Stowe T D, Kenny T W, Rugar D 2001 Phys. Rev. Lett. 87 096801
[3] Kuehn S, Loring R F, Marohn J A 2006 Phys. Rev. Lett. 96 156103
[4] Buchanan M 2007 Nat. Phys. 3 827
[5] Saitoh K, Hayashi K, Shibayama Y, Shirahama K 2010 Phys. Rev. Lett. 105 236103
[6] She J H, Balatsky A V 2012 Phys. Rev. Lett. 108 136101
[7] Pendry J B 1997 J. Phys. Condens. Matter 9 10301
[8] Volokitin A I, Persson B N J 2001 J. Phys. Condens. Matter 13 859
[9] Volokitin A I, Persson B N J 2002 Phys. Rev. B 65 115419
[10] Volokitin A I, Persson B N J 2003 Phys. Rev. Lett. 91 106101
[11] Volokitin A I, Persson B N J 2002 Phys. Rev. B 65 115420
[12] Volokitin A I, Persson B N J 2005 Phys. Rev. Lett. 94 086104
[13] Volokitin A I, Persson B N J 2007 Rev. Mod. Phys. 79 1291
[14] Volokitin A I, Persson B N J 2011 Phys. Rev. Lett. 106 094502
[15] Philbin T G, Leonhardt U 2009 New J. Phys. 11 033035
[16] Pendry J B 2010 New J. Phys. 12 033028
[17] Leonhardt U 2010 New J. Phys. 12 068001
[18] Pendry J B 2010 New J. Phys. 12 068002
[19] Volokitin A I, Persson B N J 2011 New J. Phys. 13 068001
[20] Philbin T G, Leonhardt U 2011 New J. Phys. 13 068002
[21] Silveririnha M G 2014 New J. Phys. 16 063011
[22] Manjavacas A, García de Abajo F J 2010 Phys. Rev. Lett. 105 113601
[23] Manjavacas A, García de Abajo F J 2010 Phys. Rev. A 82 063827
[24] Zhao R, Manjavacas A, García de Abajo F J, Pendry J B 2012 Phys. Rev. Lett. 109 123604
[25] Bercegol H, Lehoucq R 2015 Phys. Rev. Lett. 115 090402
[26] Intravaia F, Behunin R O, Dalvit D A R 2014 Phys. Rev. A 89 050101
[27] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[28] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Proc. Natl. Acad. Sci. U.S.A. 102 10451
[29] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[30] Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
[31] Geim A K, Novoselov K S 2007 Nat. Mater. 6 183
[32] Berger C, Song Z, Li X, Wu X, Brown N, Naud C, Mayou D, Li T, Hass J, Marchenkov A N, Conrad E H, First P N, de Heer W A 2006 Science 312 1191
[33] Freitag M, Low T, Xia F, Avouris P 2013 Nat. Photonics 7 53
[34] Stauber T, Peres N M R, Geim A K 2008 Phys. Rev. B 78 085432
[35] Falkovsky L A 2008 J. Phys. Conf. Ser. 129 012004
[36] Falkovsky L A, Pershoguba S S 2007 Phys. Rev. B 76 153410
[37] Mikhailov S A, Ziegler K 2007 Phys. Rev. Lett. 99 016803
[38] Ju L, Geng B, Horng J, Girit C, Martin M, Hao Z, Bechtel H A, Liang X, Zettl A, Shen Y R, Wang F 2011 Nat. Nanotechnol. 6 630
[39] Jablan M, Buljan H, Soljačić M 2009 Phys. Rev. B 80 245435
[40] Wang T B, Liu N H, Liu J T, Yu T B 2014 Eur. Phys. J. B 87 185
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