Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics

  • L. Brizhik Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine, Wessex Institute of Technology
  • A. P. Chetverikov Faculty of Physics, Chernyshevsky State University
  • W. Ebeling Institut f¨ur Physik, Humboldt Universit¨at
  • G. R¨opke Institut f¨ur Physik, Universit¨at Rostock
  • M. G. Velarde Instituto Pluridisciplinar, Universidad Complutense, Wessex Institute of Technology
Keywords: lattice anharmonicity, bisoliton, bisolectron, Coulomb repulsion, electron, hole, exciton, polaron, model Hamiltonian

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.

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


Published
2018-10-10
How to Cite
Brizhik, L., Chetverikov, A., Ebeling, W., R¨opkeG., & Velarde, M. (2018). Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics. Ukrainian Journal of Physics, 58(6), 562. https://doi.org/10.15407/ujpe58.06.0562
Section
Soft matter