Abstract
We numerically analyze the interaction of small-amplitude phonon waves with standing gap discrete breather (DB) in strained graphene. To make the system support gap DB, strain is applied to create a gap in the phonon spectrum. We only focus on the in-plane phonons and DB, so the issue is investigated under a quasi-one-dimensional setup. It is found that, for the longitudinal sound waves having frequencies below 6 THz, DB is transparent and thus no radiation of energy from DB takes place; whereas for those sound waves with higher frequencies within the acoustic (optical) phonon band, phonon is mainly transmitted (reflected) by DB, and concomitantly, DB radiates its energy when interacting with phonons. The latter case is supported by the fact that, the sum of the transmitted and reflected phonon energy densities is noticeably higher than that of the incident wave. Our results here may provide insight into energy transport in graphene when the spatially localized nonlinear vibration modes are presented.
Similar content being viewed by others
References
A.K. Geim, Angew. Chem. Int. Edit. 50, 6966 (2011)
K.S. Novoselov, Angew. Chem. Int. Edit. 50, 6986 (2011)
J.H. Los, K.V. Zakharchenko, M.I. Katsnelson, A. Fasolino, Phys. Rev. B 91, 045415 (2015)
E. Ganz, A.B. Ganz, L.-M. Yang, M. Dornfeld, Phys. Chem. Chem. Phys. 19, 3756 (2017)
Yu.A. Baimova, S.V. Dmitriev, A.V. Savin, Yu.S. Kivshar, Phys. Solid State 54, 866 (2012)
A.V. Savin, Y.S. Kivshar, B. Hu, Phys. Rev. B 82, 195422 (2010)
N. Li, J. Ren, L. Wang, G. Zhang, P. Hanggi, B. Li, Rev. Mod. Phys. 84, 1045 (2012)
M. Madovan, Nature 503, 209 (2013)
B. Li, L. Wang, G. Casati, Appl. Phys. Lett. 88, 143501 (2006)
K. Joulain, J. Drevillon, Y. Ezzahri, J. Ordonez-Miranda, Phys. Rev. Lett. 116, 200601 (2016)
B. Li, L. Wang, G. Casati, Phys. Rev. Lett. 93, 184301 (2004)
B. Liu, J.A. Baimova, C.D. Reddy, S.V. Dmitriev, W.K. Law, X.Q. Feng, K. Zhou, Carbon 79, 236 (2014)
B. Liu, C.D. Reddy, J. Jiang, H. Zhu, J.A. Baimova, S.V. Dmitriev, K. Zhou, J. Phys. D: Appl. Phys. 47, 165301 (2014)
S. Hu, M. An, N. Yang, B. Li, Small 13, 1602726 (2017)
Z. Duan, D. Liu, G. Zhang, Q. Li, C. Liu, S. Fan, Nanoscale 9, 3133 (2017)
L. Wang, B. Li, Phys. Rev. Lett. 99, 177208 (2007)
A. Fornieri, C. Blanc, R. Bosisio, S. D’Ambrosio, F. Giazotto, Nat. Nanotechnol. 11, 258 (2016)
S. Murad, I.K. Puri, Appl. Phys. Lett. 102, 193109 (2013)
S. Lepri, R. Livi, A. Politi, Phys. Rep. 377, 1 (2003)
A. Dhar, Adv. Phys. 57, 457 (2008)
C.-W. Chang, in Thermal transport in low dimensions, Lecture notes in physics (Springer, 2016), Vol. 921, pp. 305–338
V. Lee, C.-H. Wu, Z.-X. Lou, W.-L. Lee, C.-W. Chang, Phys. Rev. Lett. 118, 135901 (2017)
J. Lee, J. Lim, P. Yang, Nano Lett. 15, 3273 (2015)
Y.R. Koh, M. Shirazi-Hd, B. Vermeersch, A.M.S. Mohammed, J. Shao, G. Pernot, J.-H. Bahk, M.J. Manfra, A. Shakouri, Appl. Phys. Lett. 109, 243107 (2016)
D. Xiong, Phys. Rev. E 95, 042127 (2017)
D. Xiong, Europhys. Lett. 113, 14002 (2016)
B. Liu, F. Meng, C.D. Reddy, J.A. Baimova, N. Srikanth, S.V. Dmitriev, K. Zhou, RSC Adv. 5, 29193 (2015)
A. A. Sokolov, A.M. Krivtsov, W.H. Muller, Phys. Mesomech. 20, 305 (2017)
V.A. Kuzkin, A.M. Krivtsov, Phys. Solid State 59, 1051 (2017)
V.A. Kuzkin, A.M. Krivtsov, Dokl. Phys. 62, 85 (2017)
M.B. Babenkov, A.M. Krivtsov, D.V. Tsvetkov, Phys. Mesomech. 19, 282 (2016)
A.M. Krivtsov, Dokl. Phys. 60, 407 (2015)
V.A. Kuzkin, A.M. Krivtsov, Phys. Status Solidi B 252, 1664 (2015)
V.A. Kuzkin, A.M. Krivtsov, J. Phys.: Condens. Matter 29, 505401 (2017)
A.V. Savin, E.A. Korznikova, S.V. Dmitriev, E.G. Soboleva, Comput. Mater. Sci. 135, 99 (2017)
A.V. Savin, E.A. Korznikova, S.V. Dmitriev, Lett. Mater. 6, 77 (2016)
A.V. Savin, E.A. Korznikova, S.V. Dmitriev, Phys. Rev. B 92, 035412 (2015)
A.A. Le-Zakharov, A.M. Krivtsov, Dokl. Phys. 53, 261 (2008)
A.V. Savin, Y.A. Kosevich, Phys. Rev. E 89, 032102 (2014)
A.V. Savin, Yu.S. Kivshar, Phys. Rev. B 96, 064307 (2017)
K.P. Katin, A.I. Podlivaev, Phys. Solid State 52, 436 (2010)
A.I. Podlivaev, K.P. Katin, D.A. Lobanov, L.A. Openov, Phys. Solid State 53, 215 (2011)
M.M. Maslov, K.P. Katin, Chem. Phys. 387, 66 (2011)
A.I. Podlivaev, K.P. Katin, JETP Lett. 92, 52 (2010)
A.S. Dolgov, Sov. Phys. Solid State 28, 907 (1986)
A.J. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988)
S. Flach, C.R. Willis, Phys. Rep. 295, 181 (1998)
S. Flach, A.V. Gorbach, Phys. Rep. 467, 1 (2008)
S.V. Dmitriev, E.A. Korznikova, Yu.A. Baimova, M.G. Velarde, Phys. Usp. 59, 446 (2016)
Y. Yamayose, Y. Kinoshita, Y. Doi, A. Nakatani, T. Kitamura, Europhys. Lett. 80, 40008 (2007)
Y. Kinoshita, Y. Yamayose, Y. Doi, A. Nakatani, T. Kitamura, Physica D 77, 024307 (2008)
T. Shimada, D. Shirasaki, Y. Kinoshita, Y. Doi, A. Nakatani, T. Kitamura, Physica D 239, 407 (2010)
T. Shimada, D. Shirasaki, T. Kitamura, Phys. Rev. B 81, 035401 (2010)
L.Z. Khadeeva, S.V. Dmitriev, Y.S. Kivshar, JETP Lett. 94, 539 (2011)
J.A. Baimova, S.V. Dmitriev, K. Zhou, Europhys. Lett. 100, 36005 (2012)
Y. Doi, A. Nakatani, J. Solid. Mech. Mater. Eng. 6, 71 (2012)
E.A. Korznikova, A.V. Savin, Y.A. Baimova, S.V. Dmitriev, R.R. Mulyukov, JETP Lett. 99, 222 (2012)
E.A. Korznikova, J.A. Baimova, S.V. Dmitriev, Europhys. Lett. 102, 60004 (2013)
G.M. Chechin, I.P. Lobzenko, Lett. Mater. 4, 226 (2014)
J.A. Baimova, E.A. Korznikova, I.P. Lobzenko, S.V. Dmitriev, Rev. Adv. Mater. Sci. 42, 68 (2015)
S.V. Dmitriev, J. Micromech. Mol. Phys. 1, 1630001 (2016)
Y. Doi, A. Nakatani, Lett. Mater. 6, 49 (2016)
V. Hizhnyakov, M. Klopov, A. Shelkan, Phys. Lett. A 380, 1075 (2016)
I.P. Lobzenko, Lett. Mater. 6, 73 (2016)
I.P. Lobzenko, G.M. Chechin, G.S. Bezuglova, Yu.A. Baimova, E.A. Korznikova, S.V. Dmitriev, Phys. Solid State 58, 633 (2016)
R.T. Murzaev, D.V. Bachurin, E.A. Korznikova, S.V. Dmitriev, Phys. Lett. A 381, 1003 (2017)
E. Barani, I.P. Lobzenko, E.A. Korznikova, E.G. Soboleva, S.V. Dmitriev, K. Zhou, A.M. Marjaneh, Eur. Phys. J. B 90, 38 (2017)
S.V. Dmitriev, J.A. Baimova, E.A. Korznikova, A.P. Chetverikov, in Nonlinear excitations in graphene and other carbon nano-polymorphs. Understanding complex systems. nonlinear phenomena in biology, optics and condensed matter, edited by. J.F.R. Archilla et al. (Springer, Cham, 2018), Vol. 2
E. Barani, E.A. Korznikova, A.P. Chetverikov, K. Zhou, S.V. Dmitriev, Phys. Lett. A 381, 3553 (2017)
A. Fraile, E.N. Koukaras, K. Papagelis, N. Lazarides, G.P. Tsironis, Chaos Solitons Fractals 87, 262 (2016)
D. Xiong, J. Zhang, Lett. Mater. 6, 27 (2016)
D. Xiong, D. Saadatmand, S.V. Dmitriev, Phys. Rev. E 96, 042109 (2017)
G.P. Tsironis, A.R. Bishop, A.V. Savin, A.V. Zolotaryuk, Phys. Rev. E 60, 6610 (1999)
G.P. Tsironis, S. Aubry, Phys. Rev. Lett. 77, 5225 (1996)
T. Jin, J. Yu, N. Zhang, H. Zhao, Phys. Rev. E 96, 022116 (2017)
I. Evazzade, I.P. Lobzenko, E.A. Korznikova, I.A. Ovid’Ko, M.R. Roknabadi, S.V. Dmitriev, Phys. Rev. B 95, 035423 (2017)
F. Geniet, J. Leon, Phys. Rev. Lett. 89, 134102 (2002)
R. Khomeriki, S. Lepri, S. Ruffo, Phys. Rev. E 70, 066626 (2004)
P.G. Kevrekidis, S.V. Dmitriev, S. Takeno, A.R. Bishop, E.C. Aifantis, Phys. Rev. E 70, 066627 (2004)
D. Saadatmand, D. Xiong, V.A. Kuzkin, A.M. Krivtsov, A.V. Savin, S.V. Dmitriev, Phys. Rev. E 97, 022217 (2018)
D.W. Brenner, Phys. Rev. B 42, 9458 (1990)
N.K. Voulgarakis, G. Hadjisavvas, P.C. Kelires, G.P. Tsironis, Phys. Rev. B 69, 113201 (2004)
G.M. Chechin, S.V. Dmitriev, I.P. Lobzenko, D.S. Ryabov, Phys. Rev. B 90, 045432 (2014)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Evazzade, I., Roknabadi, M.R., Behdani, M. et al. Interaction of longitudinal phonons with discrete breather in strained graphene. Eur. Phys. J. B 91, 163 (2018). https://doi.org/10.1140/epjb/e2018-90055-3
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2018-90055-3