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Current issue   Ukr. J. Phys. 2014, Vol. 58, N 6, p.562-572
https://doi.org/10.15407/ujpe58.06.0562    Paper

Brizhik L.1,2, Chetverikov A.P.3, Ebeling W.4, Röpke G.5, Velarde M.G.6,2

1 Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrolohichna Str., Kyiv 03680, Ukraine; e-mail: brizhik@bitp.kiev.ua)
2 Wessex Institute of Technology
(Ashurst, Southampton SO40 7AA, UK)
3 Faculty of Physics, Chernyshevsky State University
(83, Astrakhanskaya Str., Saratov 410012, Russia)
4 Institut für Physik, Humboldt Universität
(Newtonstrasse 15, Berlin 12489, Germany)
5 Institut für Physik, Universität Rostock
(Rostock 18051, Germany)
6 Instituto Pluridisciplinar, Universidad Complutense
(Paseo Juan XXIII, 1, Madrid 28040, Spain)

Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics

Section: Soft matter
Original Author's Text: English

Abstract: We show that, in anharmonic one-dimensional lattices, the pairing of electrons or holes in a localized bisoliton (called also bisolectron) state is possible due to a coupling between the charges and the lattice deformation that can overcome the Coulomb repulsion. We show that bisolitons are dynamically stable up to the sound velocities in lattices with cubic or quartic anharmonicities, and have finite values of energy and momentum in the whole interval of bisoliton velocities up to the sound velocity in the chain. We calculate the bisoliton binding energy and the critical value of Coulomb repulsion at which the bisoliton becomes unstable and decays into two independent electrosolitons. We estimate these energies for chain parameters that are typical of biological macromolecules and some quasi-one-dimensional conducting systems and show that the Coulomb repulsion in such systems is relatively weak as compared with the binding energy. Our analytical results are in a good agreement with the results of numerical simulations in a broad interval of the parameter values.

Key words: lattice anharmonicity, bisoliton, bisolectron, Coulomb repulsion, electron, hole, exciton, polaron, model Hamiltonian.

References:

  1. L.D. Landau, Phys. Z. Sowjetunion. 3, 664 (1933).
  2. S.I. Pekar, Untersuchungen ¨uber die Elektronentheorie (Akademie, Berlin, 1954).
  3. E.I. Rashba, Izv. Akad. Nauk USSR, Ser. Fiz. 21, 37 (1957).
  4. A.S. Alexandrov and N. Mott, Polarons and Bipolarons (World Scientific, Singapore, 1995).
  5. Polarons in Advanced Materials, edited by A.S. Alexandrov (Springer, Berlin, 2007).
  6. A.S. Davydov, Solitons in Molecular Systems (Reidel, Dordrecht, 1991). https://doi.org/10.1007/978-94-011-3340-1
  7. Davydov's Soliton Revisited. Self-Trapping of Vibrational Energy in Proteins, edited by A.L. Christiansen and A.C. Scott (Plenum Press, New York, 1983).
  8. A.C. Scott, Phys. Rep. 217, 1 (1992). https://doi.org/10.1016/0370-1573(92)90093-F
  9. L.S. Brizhik and A.S. Davydov, J. Low Temp. Phys. 10, 748 (1984).
  10. L.S. Brizhik and A.S. Davydov, J. Low Temp. Phys. 10, 748 (1984).
  11. L.S. Brizhik, J. Low Temp. Phys. 12, 437 (1986).
  12. A.S. Davydov and A.V. Zolotaryuk, Phys. Stat. Sol. (b) 115, 115 (1983). https://doi.org/10.1002/pssb.2221150113
  13. A.S. Davydov and A.V. Zolotaryuk, Phys. Lett. A 94, 49 (1983). https://doi.org/10.1016/0375-9601(83)90285-2
  14. A. S. Davydov and A. V. Zolotaryuk, Phys. Scripta 30, 426 (1984). https://doi.org/10.1088/0031-8949/30/6/010
  15. M.G. Velarde, L Brizhik, A.P. Chetverikov, L. Cruzeiro, V. Ebeling, and G. R¨o pke, Int. J. Quant. Chem. 112, 551(2012). https://doi.org/10.1002/qua.23008
  16. M.G. Velarde, L. Brizhik, A.P. Chetverikov, L. Cruzeiro, V. Ebeling, and G. R¨opke, Int. J. Quant. Chem. 112, 2591 (2012). https://doi.org/10.1002/qua.23282
  17. M. Toda, Theory of Nonlinear Lattices (Springer, New York, 1989). https://doi.org/10.1007/978-3-642-83219-2
  18. M. Toda, Nonlinear Waves and Solitons (KTK Sci. Publ., Tokyo, 1989).
  19. D.J. Korteweg and G. de Vries, Phil. Mag. 39, 442 (1895).
  20. C.I. Christov, G.A. Maugin, and M.G. Velarde, Phys. Rev. E 54, 3621 (1996). https://doi.org/10.1103/PhysRevE.54.3621
  21. M. Remoissenet, Waves Called Solitons (Springer, Berlin, 1999). https://doi.org/10.1007/978-3-662-03790-4
  22. V.I. Nekorkin and M. G. Velarde, Synergetic Phenomena in Active Lattices. Patterns, Waves, Solitons, Chaos (Springer, Berlin, 2002). https://doi.org/10.1007/978-3-642-56053-8
  23. T. Dauxois and M. Peyrard, Physics of Solitons (Cambridge Univ. Press, Cambridge, 2006).
  24. L. Cruzeiro, J.C. Eilbeck, J.L. Marin, and F.M. Russell, Eur. Phys. J. B 42, 95 (2004). https://doi.org/10.1140/epjb/e2004-00360-1
  25. M.G. Velarde, Ch. Neissner, Int. J. Bifurcation Chaos, 18, 885 (2008). https://doi.org/10.1142/S0218127408020744
  26. M.G. Velarde, W. Ebeling, A.P. Chetverikov, Int. J. Bifurcation Chaos 18, 3815 (2008). https://doi.org/10.1142/S0218127408022767
  27. D. Hennig, M.G. Velarde, W. Ebeling, and A.P. Chetverikov, Phys. Rev. E 78, 066606 (2008). https://doi.org/10.1103/PhysRevE.78.066606
  28. M.G. Velarde, J. Comput. Appl. Math. 233, 1432 (2010). https://doi.org/10.1016/j.cam.2008.07.058
  29. W. Ebeling, M.G. Velarde, and A.P. Chetverikov, Cond. Matt. Phys. 12, 633 (2009). https://doi.org/10.5488/CMP.12.4.633
  30. L. Brizhik, A.P. Chetverikov, W. Ebeling, G. R¨o pke, and M. G. Velarde, Phys. Rev. B 85, 245105 (2012). https://doi.org/10.1103/PhysRevB.85.245105
  31. L. Brizhik, L. Cruzeiro-Hansson, A. Eremko, and Yu. Olkhovska, Phys. Rev. B 61, 1129 (2000). https://doi.org/10.1103/PhysRevB.61.1129
  32. L. Brizhik, L. Cruzeiro-Hansson, A. Eremko, and Yu. Olkhovska, Synth. Met. 109, 113 (2000). https://doi.org/10.1016/S0379-6779(99)00209-X
  33. V.D. Lakhno and V.B. Sultanov, J. Appl. Phys. 112, 064701 (2012). https://doi.org/10.1063/1.4752875
  34. E.G. Wilson, J. Phys. C 16 6739 (1983).
  35. K.J. Donovan and E.G. Wilson, Phil. Mag. B 44, 9 (1981). https://doi.org/10.1080/01418638108222364
  36. A.A. Gogolin, Pis'ma Zh. Eksp. Teor. Phys. 43, 395 (1986)
  37. Electronic Properties of Inorganic Quasi-One-Dimensional Compounds, edited by P. Monceau, Part II, (Reidel, Dordrecht, 1985).
  38. B.G. Streetman and B. Sanjay, Solid State Electronic Devices (Prentice-Hall, Englewood Cliff, NJ, 2000).
  39. Y. Zhang, X. Ke, C. Chen, and P.C. Kent, Phys. Rev. B 80, 024303 (2009).
  40. Lead Selenide (PbSe) Crystal Structure, Lattice Parameters, Thermal Expansion, edited by O. Madelung, U. R¨ossler, and M. Schultz (Springer, Berlin, 2005), Vol. 41C, available at: http://www.springermaterials.com.
  41. J. Androulakis, Y. Lee, I. Todorov et al., Phys. Rev. B 83, 195209 (2011). https://doi.org/10.1103/PhysRevB.83.195209
  42. C. Falter and G.A. Hoffmann, Phys. Rev. B 64, 054516 (2001). https://doi.org/10.1103/PhysRevB.64.054516
  43. K.-P. Bohnen, R. Heid, and M. Krauss, Europhys. Lett. 64, 104 (2003). https://doi.org/10.1209/epl/i2003-00143-x
  44. R.J. McQueeney, Y. Petrov, T. Egami et al., Phys. Rev. Lett. 82, 628 (1999). https://doi.org/10.1103/PhysRevLett.82.628
  45. T.P. Devereaux, T. Cuk, Z.-X. Shen, and N. Nagaosa, Phys. Rev. Lett. 93, 117004 (2004). https://doi.org/10.1103/PhysRevLett.93.117004
  46. J.-H. Chung, T. Egami, R.J. McQueeney et al., Phys. Rev. B 67, 014517 (2003). https://doi.org/10.1103/PhysRevB.67.014517