Abstract.
We discuss here the thermal excitation of soliton-like supersonic, intrinsic localized modes in two-dimensional monolayers of atoms imbedded into a heat bath. These excitations induce local electrical polarization fields at the nano-scale in the lattice which influence electron dynamics, thus leading to a new form of trapping. We study the soliton-mediated electron dynamics in such systems at moderately high temperatures and calculate the density of embedded electrons in a suitable adiabatic approximation.
Similar content being viewed by others
References
N. Zabusky, Chaos 15, 015102 (2005), and references therein
M. Toda, Theory of Nonlinear Lattices, 2nd edn. (Springer-Verlag, New York, 1989)
E. Arevalo, Yu. Gaididei, F.G. Mertens, Eur. Phys. J. B 27, 63 (2002)
E. Arevalo, F.G. Mertens, Yu. Gaididei, A.R. Bishop, Phys. Rev. E 67, 016610 (2003)
M.G. Velarde, W. Ebeling, A.P. Chetverikov, Int. J. Bifurc. Chaos 15, 245 (2005)
A.P. Chetverikov, W. Ebeling, M.G. Velarde, Eur. Phys. J. B 51, 87 (2006)
M.G. Velarde, W. Ebeling, D. Hennig, C. Neissner, Int. J. Bifurc. Chaos 16, 1035 (2006)
D. Hennig, C. Neissner, M.G. Velarde, W. Ebeling, Phys. Rev. B 73, 024306 (2006)
A.P. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, Contr. Plasma Phys. 47, 465 (2007)
D. Hennig, A.P. Chetverikov, M.G. Velarde, W. Ebeling, Phys. Rev. E 76, 046602 (2007)
M.G. Velarde, W. Ebeling, A.P. Chetverikov, D. Hennig, Int. J. Bifurc. Chaos 18, 521 (2008)
M.G. Velarde, W. Ebeling, A.P. Chetverikov, Int. J. Bifurc. Chaos 18, 3815 (2008)
D. Hennig, M.G. Velarde, A.P. Chetverikov, W. Ebeling, Phys. Rev. E 18, 521 (2008)
A.P. Chetverikov, W. Ebeling, M.G. Velarde, Eur. Phys. J. B 70, 117 (2009)
W. Ebeling, M.G. Velarde, A.P. Chetverikov, Cond. Matter Phys. 12, 1 (2009)
M.G. Velarde, W. Ebeling, A.P. Chetverikov, in From Physics to Control through an Emergent View, edited by L. Fortuna, A. Fradkov, M. Frasca (World Scientific, Singapore, 2010), pp. 8-13
H. Linde, M.G. Velarde, W. Waldhelm, A. Wierschem, J. Coll. Interface Sci. 236, 214 (2001)
H. Linde, M.G. Velarde, W. Waldhelm, K. Loeschcke, A. Wierschem, Ind. Eng. Chem. Res. 44, 1396 (2005)
E.N. Kalaidin, S.Yu. Vlaskin, E.A. Demekhin, S. Kalladiasis, Doklady Phys. 51, 37 (2006)
A.A. Nepomnyashchy, M.G. Velarde, P. Colinet, Interfacial Phenomena and Convection (Chapman & Hall/CRC, London, 2002), Chap. 5
Y.V. Kartashov, B.A. Malomed, V.A. Vysloukh, L. Torner, Opt. Lett. 34, 770 (2009)
N.K. Efremidis, J.W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D.N. Christodoulides, M. Segev, in Nonlinearities of Periodic Structures and Metamaterials, edited by C. Denz, S. Flach, Yu.S. Kivshar (Springer, Berlin, 2009)
J.W. Fleischer, M. Segev, N.K. Efremidis, D.N. Christodoulides, Nature 422, 147 (2003)
D.B. Duncan, J.C. Eilbeck, H.C. Walshaw, V.E. Zakharov, Phys. Lett. A 158, 107 (1091)
Y. Gaididei, N. Flytzanis, F.G. Mertens, Physica D 82, 229 (1995)
R. Huss, F.G. Mertens, Y. Gaididei, in Fluctuation Phenomena: Disorder and Nonlinearity, edited by A.R. Bishop, S. Jimenez, L. Vazquez (World Scientific, Singapore, 1995), pp. 224-250
Yu.B. Gaididei, P.L. Christiansen, S.F. Mingalaev, Phys. Scr. 51, 289 (1995)
Y. Gaididei, R. Huss, F.G. Mertens, Eur. Phys. J. B 6, 257 (1998)
E.A. Ostrovskaya, S.F. Mingalaev, Yu.S. Kivshar, Yu.B. Gaididei, P.L. Christiansen, Phys. Lett. A 282, 157 (2001)
P.G. Kevrekidis, B.A. Malomed, Y.B. Gaididei, Phys. Rev. B 65, 016609 (2002)
V.M. Burlakov, S.A. Kiselev, V.N. Pyrkov, Phys. Rev. B 42, 4921 (1990)
I.A. Butt, J.A.D. Wattis, J. Phys. A: Math. Gen. 39, 4955 (2006)
I.A. Butt, J.A.D. Wattis, J. Phys. A: Math. Gen. 40, 1239 (2007)
J.L. Marin, J.C. Eilbeck, F.M. Russell, Phys. Lett. 248, 225 (1998)
F.M. Russell, J.C. Eilbeck, Eur. Phys. Lett. 78, 10004 (2007)
J.L. Marin, F.M. Russell, J.C. Eilbeck, Phys. Lett. A 281, 21 (2001)
T.Yu. Astakhova, G.A. Vinogradov, J. Phys. A: Math. Gen. 39, 3593 (2006)
W. Ebeling, V.Yu. Podlipchuk, A.A. Valuev, Physica A 217, 22 (1995)
W. Ebeling, A.A. Valuev, V.Yu. Podlipchuk, J. Molecular Liquids 73, 445 (1997)
W. Ebeling, V.Yu. Podlipchuk, M.G. Sapeshinsky, Int. J. Bifurc. Chaos 8, 755 (1998)
F. Marchesoni, C. Lucheroni, Phys. Rev. E 44, 5303 (1991)
L.D. Landau, Phys. Z. Sowjetunion 3, 664 (1933)
S.I. Pekar, Untersuchungen über die Elektronentheorie (Academic-Verlag, Berlin, 1954), and references therein
A.S. Davydov, Solitons in Molecular Systems, 2nd edn. (Reidel, Dordrecht, 1991), and references therein
L.S. Brizhik, A.S. Davydov, Phys. Stat. Sol. (b) 115, 615 (1983)
A.S. Davydov, Phys. Stat. Sol. (b) 138, 559 (1986)
Davydov’s Solitons Revisited, Self-trapping of Vibrational Energy in Protein, edited by P.L. Christiansen, A.C. Scott (Plenum Press, New York, 1983)
P.S. Lomdahl, W.C. Kerr, Phys. Rev. Lett. 55, 1235 (1985)
A.C. Scott, Phys. Rep. 217, 1 (1992)
L. Cruzeiro-Hansson, S. Takeno, Phys. Rev. E 56, 894 (1997), and references therein
A.V. Zolotaryuk, K.H. Spatschek, A.V. Savin, Phys. Rev. B 54, 266 (1996)
L. Brizhik, B. Piette, W.J. Zakrewski, Ukrain. Fiz. Zh. 46, 503 (2001)
L. Brizhik, A. Eremko, B. Piette, W.J. Zakrewski, Ukrain. Fiz. Zh. 47, 890 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chetverikov, A., Ebeling, W. & Velarde, M. Soliton-like excitations and solectrons in two-dimensional nonlinear lattices. Eur. Phys. J. B 80, 137–145 (2011). https://doi.org/10.1140/epjb/e2010-10604-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2010-10604-0