Discrete breathers above phonon spectrum

V. Hizhnyakov, A. Shelkan, M. Haas, M. Klopov show affiliations and emails
Accepted  24 March 2016
Citation: V. Hizhnyakov, A. Shelkan, M. Haas, M. Klopov. Discrete breathers above phonon spectrum. Lett. Mater., 2016, 6(1) 61-72
BibTex   https://doi.org/10.22226/2410-3535-2016-1-61-72

Abstract

It is shown that in some metals (Ni, Nb, Fe, Cu) may exist discrete breathers with frequencies above the top of the phonon spectrum. These excitations are mobile: they may propagate along the crystallographic directions transferring energy of >~ 1 eV over large distances. The discrete breathers with the frequencies above the top of the phonon bands may also exist in covalent crystals (diamond, Si and Ge). It is also found that in monatomic chains and planes (e.g. in graphene), the transverse discrete breathers may be excited above the spectrum of corresponding phonons. Although these vibrations are in resonance with longitudinal (chain) or in-plane (graphene) phonons the lifetime of them may be very long. 1. Introduction It is already a well known fact that in crystal lattices may exist long living anharmonic modes of rather high energy >~ 1 eV. These excitations are called as discrete breathers (DBs), intrinsic localized modes, vibrational solitons, or quodons [2, 4, 7, 11, 13, 14, 16, 17, 29, 31, 32, 34, 42, 43, 46, 47, 48, 51, 52]. In numerical studies of DBs different two-body potential models (Morse, Lennard-Jones, Born-Mayer-Coulomb and other potentials) have been used. All these potentials show strong softening at increasing vibrational amplitudes. Therefore the frequencies of DBs, found in these studies, drop down from the optical band(s) into the phonon gaps, if such gaps exist in the spectrum (see, e.g. Refs. [26, 28, 30]).

References (56)

1. V. Adamyan and V. Zavalniuk, J. Phys.: Condens. Matter 23 (2011) 015402.
2. Archilla, J. F. R., Coelho, S. M. M., Auret, F. D., Dubinko, V. I., Hizhnyakov, V.: Long range annealing of defects in germanium by low energy plasma ions. Physica D 297 (2015) 56 - 61.
3. J. A. Baimova, S. V. Dmitriev, K. Zhou, EPL 100 (2012) 36005.
4. Bickham, S. R., Sievers, A. J., Takeno, S.: Numerical measurements of the shape and dispersion relation for moving one-dimensional anharmonic localized modes. Phys. Rev. B 45 (18), 10, 344 - 10, 347 (1992).
5. M. Peyrard and A. R. Bishop, Phys. Rev. Lett., 62 (1989) 2755.
6. S. Cadet, Phys. Lett. A 121 (1987) 77.
7. Campbell, D. K., Flach, S., Kivshar, Y. S.: Localizing energy through nonlinearity and discreteness. Physics Today 57 (1), 43 - 49 (2004).
8. Chamati, H., Papanicolaou, N. I., Mishin, Y., Papaconstantopoulos, D. A.: Embedded-atom potential for Fe and its application to self-diffusion on Fe (1 0 0). Surf. Sci. 600 (9), 1793 - 1803 (2006).
9. Daw, M. S., Baskes, M. I.: Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals. Phys. Rev. Lett. 50 (17), 1285 - 1288 (1983).
10. Daw, M. S., Baskes, M. I.: Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29 (12), 6443 - 6453 (1984).
11. Dolgov, A. S.: The localization of vibrations in a nonlinear crystal structure. Sov. Phys. Solid State 28, 907 - 910 (1986).
12. A. Fasolino, J. H. Los and M. I. Katsenelson, Nature Materials 6 (2007) 858.
13. Flach, S., Gorbach, A.: Discrete breathers - Advances in theory and applications. Phys. Rep. 467 (1-3), 1 - 116 (2008).
14. Flach, S., Willis, C. R.: Discrete breathers. Phys. Rep. 295 (5), 181 - 264 (1998).
15. Haas, M., Hizhnyakov, V., Shelkan, A., Klopov, M., Sievers, A. J.: Prediction of high-frequency intrinsic localized modes in Ni and Nb. Phys. Rev. B 84, 144, 303 (1-8) (2011).
16. Henry, B. R.: Local modes and their application to the analysis of polyatomic overtone spectra. J. Phys. Chem. 80 (20), 2160 - 2164 (1976).
17. Henry, B. R., Kjaergaard, H. G.: Local modes. Can. J. Chem. 80 (12), 1635 - 1642 (2002).
18. Hizhnyakov, V.: Relaxation jumps of strong vibration. Phys. Rev. B 53, 13, 981 - 13, 984 (1996).
19. V. V. Hizhnyakov, M. Haas, A. Shelkan and M. Klopov, in: J. F. R. Archilla, N. Jiménez, V. J. Sánchez-Morcillo, L. M. Garca-Raffi (Eds.), Quodons in mica: nonlinear localized travelling excitations in crystals, Springer Series in Material Science, 221 (2015) 229.
20. Hizhnyakov, V., Haas, M., Shelkan, A., Klopov, M.: Theory and molecular dynamics simulations of intrinsic localized modes and defect formation in solids. Phys. Scr. 89, 044, 003 (1-5) (2014).
21. Hizhnyakov, V., Klopov, M., Shelkan, A.: Transverse intrinsic localized modes in monatomic chain and in graphene. Phys. Lett. A 380 (9-10), 1075 - 1081 (2016).
22. Hizhnyakov, V., Nevedrov, D., Sievers, A. J.: Quantum properties of intrinsic localized modes. Physica B 316 - 317, 132 - 135 (2002).
23. Hizhnyakov, V., Shelkan, A., Klopov, M.: Self-consistent theory of intrinsic localized modes: Application to monatomic chain. Phys. Lett. A 357 (4-5), 393 - 396 (2006).
24. Hizhnyakov, V., Shelkan, A., Klopov, M., Kiselev, S. A., Sievers, A. J.: Linear local modes induced by intrinsic localized modes in a monatomic chain. Phys. Rev. B 73, 224, 302 (1-6) (2006).
25. Hizhnyakov, V., Shelkan, A., Klopov, M., Sievers, A. J.: Localized vibrations in perfect anharmonic lattices: Trapping on phonons. J. Lumin. 128 (5-6), 995 - 997 (2008).
26. Khadeeva, L. Z., Dimitriev, S. V.: Discrete breathers in crystals with NaCl structure. Phys. Rev. B 81, 214, 306 (1-8) (2010).
27. L. Z. Khadeeva, S. V. Dmitriev, Yu. S. Kivshar, JETP Lett. 94 (2011) 539.
28. Kiselev, S. A., Bickham, S. R., Sievers, A. J.: Anharmonic gap modes in a perfect 1-d diatomic lattice for standard two-body nearest-neighbor potentials. Phys. Rev. B 48 (18), 13, 508 - 13, 511 (1993).
29. Kiselev, S. A., Rupasov, V. I.: Stationary vibrational modes of a polyatomic chain of particles interacting via an even order potential. Phys. Lett. A 148 (6-7), 355 - 358 (1990).
30. Kiselev, S. A., Sievers, A. J.: Generation of intrinsic vibrational gap modes in three-dimensional ionic crystals. Phys. Rev. B 55 (9), 5755 - 5758 (1997).
31. Kosevich, A. M., Kovalev, A. S.: Self-localization of vibrations in a one-dimensional anharmonic chain. Sov. Phys. JETP 40 (5), 891 - 896 (1974).
32. Lai, R., Sievers, A. J.: Nonlinear nanoscale localization of magnetic excitations in atomic lattices. Phys. Rep. 314 (3), 147 - 236 (1999).
33. Los, J. H., Fasolino, A.: Intrinsic long-range bond-order potential for carbon: Performance in Monte Carlo simulations of graphitization. Phys. Rev. B 68, 024, 107 (1-14) (2003).
34. MacKay, R. S., Aubry, S.: Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators. Nonlinearity 7 (6), 1623 - 1644 (1994).
35. P. Maniadis, B. S. Alexandrov, A. R. Bishop, and K. O. Rasmussen, Phys. Rev. E, 33 (2011) 011904.
36. L. I. Manevitch and A. V. Savin, Phys. Rev. E, 55 (1997) 4713.
37. Maradudin, A. A.: Theoretical and Experimental Aspects of the Effects of Point Defects and Disorder of the Vibrations of Crystals. In: F. Seitz, D. Turnbull (eds.) Solid State Physics, vol. 18, 19. Academic Press, New York (1966).
38. Maradudin, A. A., Montroll, E. W., Weiss, G. S., Ipatova, I. P.: Theory of Lattice Dynamics in the Harmonic Approximation. In: H. Ehrenreich, F. Seitz, D. Turnbull (eds.) Solid State Physics, Suppl 3, 2nd edn. Academic Press, New York (1971).
39. N. D. Mermin, Phys. Rev. 176 (1968) 250.
40. J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth and S. Roth, Nature 446 (2007) 60.
41. Mishin, Y., Mehl, M. J., Papaconstantopoulos, D. A., Voter, A. F., Kress, J. D.: Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations. Phys. Rev. B 63, 224, 106 (1-16) (2001).
42. Ovchinnikov, A. A., Erihjman, N. S.: On vibrational energy localization at high levels of excitation. Vibrational excitons. Sov. Phys. Usp. 25 (10), 738 - 755 (1982).
43. Page, J. B.: Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems. Phys. Rev. B 41 (11), 7835 - 7838 (1990).
44. S. Luccioli, A. Imparato, S. Lepri, F. Piazza and A. Torcini, Phys. Biol., 8 (2011) 046008.
45. F. M. Russell and C. J. Eilbeck, Europhysics Letters, 78 (2007) 10004.
46. Sage, M. L., Jortner, J.: Bond modes. Adv. Chem. Phys. 47, 293 - 323 (1981).
47. Sandusky, K. W., Page, J. B., Schmidt, K. E.: Stability and motion of intrinsic localized modes in nonlinear periodic lattices. Phys. Rev. B 46 (10), 6161 - 6168 (1992).
48. Sato, M., Hubbard, B. E., Sievers, A. J.: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays. Rev. Mod. Phys. 78, 137 - 157 (2006).
49. A. V. Savin, L. I. Manevich, P. L. Christiansen and A. V. Zolotaryuk, Phys.-Usp. 42 (1999) 245.
50. Shelkan, A., Hizhnyakov, V., Klopov., M.: Self-consistent potential of intrinsic localized modes: Application to diatomic chain. Phys. Rev. B 75, 134, 304 (1-6) (2007).
51. Sievers, A. J., Page, J. B.: Unusual anharmonic local mode systems. In: G. K. Horton, A. A. Maradudin (eds.) Dynamical Properties of Solids: Phonon Physics The Cutting Edge, vol. VII, pp. 137 - 255. North Holland, Amsterdam (1995).
52. Sievers, A. J., Takeno, S.: Intrinsic Localized Modes in Anharmonic Crystals. Phys. Rev. Lett. 61 (8), 970 - 973 (1988).
53. Tersoff, J.: New empirical model for the structural properties of silicon. Phys. Rev. Lett. 56 (6), 632 - 635 (1986).
54. Tersoff, J.: Modeling solid-state chemistry: Interatomic potentials for multicomponent systems. Phys. Rev. B 39 (8), 5566 - 5568 (1989).
55. Voulgarakis, N. K., Hadjisavvas, S., Kelires, P. C., Tsironis, G. P.: Computational investigation of intrinsic localization in crystalline Si. Phys. Rev. B 69, 113, 201 (1-4) (2004).
56. Interatomic Potentials Repository Project. http://www.ctcms.nist.gov/potentials.

Cited by (12)

1.
R.T. Murzaev, D.V. Bachurin, E.A. Korznikova, S.V. Dmitriev. Physics Letters A. 381(11), 1003 (2017). Crossref
2.
A. Rivière, S. Lepri, D. Colognesi, F. Piazza. Phys. Rev. B. 99(2) (2019). Crossref
3.
E. Barani, Elena A. Korznikova, Alexander P. Chetverikov, K. Zhou, Sergey V. Dmitriev. Physics Letters A. 381(41), 3553 (2017). Crossref
4.
P. V. Zakharov, M. D. Starostenkov, A. M. Eremin, E. A. Korznikova, S. V. Dmitriev. Phys. Solid State. 59(2), 223 (2017). Crossref
5.
E. Barani, Ivan P. Lobzenko, Elena A. Korznikova, Elvira G. Soboleva, Sergey V. Dmitriev, K. Zhou, A. Marjaneh. Eur. Phys. J. B. 90(3) (2017). Crossref
6.
Sergey V. Dmitriev. NOLTA. 8(2), 85 (2017). Crossref
7.
Elena A. Korznikova, Stepan A. Shcherbinin, Denis S. Ryabov, George M. Chechin, Evgeny G. Ekomasov, E. Barani, K. Zhou, Sergey V. Dmitriev. Phys. Status Solidi B. 256(1), 1800061 (2019). Crossref
8.
K.A. Krylova, J.A. Baimova, R.T. Murzaev, R.R. Mulyukov. Physics Letters A. 383(14), 1583 (2019). Crossref
9.
Sergey V. Dmitriev, Julia A. Baimova, Elena A. Korznikova, Alexander P. Chetverikov. Understanding Complex Systems: Nonlinear Systems, Vol. 2, Chapter 7, p.175 (2018). Crossref
10.
Alexander V. Savin, Elena A. Korznikova, Sergey V. Dmitriev. Phys. Rev. B. 99(23) (2019). Crossref
11.
O. Bachurina. Modelling Simul. Mater. Sci. Eng. 27(5), 055001 (2019). Crossref
12.
O. V. Bachurina, R. T. Murzaev, A. A. Kudreyko, S. V. Dmitriev, D. V. Bachurin. Eur. Phys. J. B. 95(7) (2022). Crossref

Similar papers