Abstract
The pairing of electrons in harmonic and anharmonic one-dimensional lattices is studied with account of the electron-lattice interaction. It is shown that in harmonic lattices binding of electrons in a bound localized state called bisoliton, takes place. It is also shown that bisolitons in harmonic lattices can propagate with velocity below the velocity of the sound. Similarly, binding of electrons in singlet spin state, called bisolectron, takes place in anharmonic lattices. It is shown that the account of the lattice anharmonicity leads to the stabilization of bisolectron dynamics: bisolectrons are dynamically stable up to the sound velocity in lattices with cubic or quartic anharmonicities and can also be supersonic. They have finite values of energy and momentum in the whole interval of bisolectron velocities. The bisolectron binding energy and critical value of the Coulomb repulsion at which the bisolectron becomes unstable and decays into two independent solectrons, are calculated. The analytical results are in a good agreement with the results of numerical simulations in a broad interval of the parameter values.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alexandrov, A.S. (ed.): Polarons in Advanced Materials. Springer, New York (2008)
Alexandrov, A.S., Mott, N.F.: Polarons & Bipolarons. World Scientific, Singapore (1995)
Androulakis, J., Lee, Y., Todorov, I., Chung, D.Y., Kanatzidis, M.: High-temperature thermoelectric properties of n-type PbSe doped with Ga, In, and Pb. Phys. Rev. B 83(19), 195209 (2011)
Bohnen, K.P., Heid, R., Krauss, M.: Phonon dispersion and electron-phonon interaction for YBCO from first principle calculations. Europhys. Lett. 64(5), 104 (2003)
Brizhik, L., Chetverikov, A.P., Ebeling, W., Röpke, G., Velarde, M.G.: Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices. Phys. Rev. B 85(24), 245105 (2012)
Brizhik, L., Cruzeiro-Hansson, L., Eremko, A., Olkhovska, Y.: Polaron dynamics and Peierls-Nabarro barrier in a discrete molecular chain. Synthetic Met. 109(1), 113–116 (2000)
Brizhik, L., Eremko, A., Cruzeiro-Hansson, L., Olkhovska, Y.: Soliton dynamics and Peierls-Nabarro barrier in a discrete molecular chain. Phys. Rev. B 61(2), 1129 (2000)
Brizhik, L.S.: Bisolitons in one-dimensional molecular systems. Fiz. Nizk. Temp. 14, 437–441 (1986)
Brizhik, L.S., Davydov, A.S.: The electrosoliton pairing in soft molecular chains. Fiz. Nizk. Temp. 10(7), 748–753 (1984)
Brizhik, L.S., Eremko, A.A.: One-dimensional electron-phonon system at arbitrary coupling constant. Z. Phys. B Cond. Matt. 104(4), 771–775 (1997)
Carneiro, K., Monceau, P.: Electronic Properties of Inorganic Quasi-one-dimensional Compounds. Reidel, Dordrecht, p. 1 (1985)
Christov, C.I., Maugin, G.A., Velarde, M.G.: Well-posed Boussinesq paradigm with purely spatial higher-order derivatives. Phys. Rev. E 54(4), 3621 (1996)
Chung, J.H., Egami, T., McQueeney, R.J., Yethiraj, M., Arai, M., Yokoo, T., Petrov, Y., Mook, H.A., Endoh, Y., Tajima, S., Frost, C., Dogan, F.: In-plane anisotropy and temperature dependence of oxygen phonon modes in YBa\(_2\). Phys. Rev. B 67(1), 014517 (2003)
Cisneros-Ake, L.A., Minzoni, A.A.: Effect of hydrogen bond anharmonicity on supersonic discrete Davydov soliton propagation. Phys. Rev. E 85(2), 021925 (2012)
Cisneros-Ake, L.A., Minzoni, A.A., Velarde, M.G.: Variational approximation to electron trapping by soliton-like localized excitations in one-dimensional anharmonic lattices. In: Localized Excitations in Nonlinear Complex Systems, pp. 225–235. Springer (2014)
Clasen, R., Grosse, P., Krost, A., Levy, F., Marenkin, S.F., Richter, W., Ringelstein, N., Schmechel, R., Weiser, G., Werheit, H.e.a.: Non-Tetrahedrally bonded elements and binary compounds I. Landolt-Bornstein, New Series, Group III 17(Pt B) (1998)
Cruzeiro, L., Eilbeck, J.C., Marin, J.L., Russell, F.M.: Dynamical two electron states in a Hubbard-Davydov model. Eur. Phys. J. B 42(1), 95–102 (2004)
Dauxois, T., Peyrard, M.: Physics of Solitons. Cambridge University Press, Cambridge (2006)
Davydov, A.: Solitons in Molecular Systems. Reidel, Dordrecht (1991)
Davydov, A.S., Zolotariuk, A.V.: Autolocalized collective excitations in molecular chains with cubic anharmonicity. Phys. Status Solidi B 115(1), 115–125 (1983)
Davydov, A.S., Zolotariuk, A.V.: Solitons in molecular systems with nonlinear nearest-neighbour interactions. Phys. Lett. A 94(1), 49–51 (1983)
Davydov, A.S., Zolotariuk, A.V.: Subsonic and supersonic solitons in nonlinear molecular chains. Phys. Scripta 30(6), 426 (1984)
Devereaux, T.P., Cuk, T., Shen, Z.X., Nagaosa, N.: Anisotropic electron-phonon interaction in the cuprates. Phy. Rev. Lett. 93(11), 117004 (2004)
Donovan, K.J., Wilson, E.G.: Demonstration of an ultra-high mobility organic polymer. Phil. Mag. B 44(1), 9–29 (1981)
Ebeling, W., Velarde, M.G., Chetverikov, A.P.: Bound states of electrons with soliton-like excitations in thermal systems-adiabatic approximations. Cond. Matt. Phys. 12(4), 633–645 (2009)
Falter, C., Hoffmann, G.A.: Nonlocal electron-phonon coupling of ionic charge-fluctuation type and phonon anomalies in high-temperature superconductors. Phys. Rev. B 64(5), 054516 (2001)
Gogolin, A.A.: Drift velocity for acoustic polarons in 1D conductors. Sov. Phys. JETP 43, 511 (1986)
Hennig, D., Velarde, M., Ebeling, W., Chetverikov, A.: Compounds of paired electrons and lattice solitons moving with supersonic velocity. Phys. Rev. E 78(6), 066606 (2008)
Korteweg, D.J., De Vries, G.: On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Phil. Mag. 39(240), 422–443 (1895)
Lakhno, V.D., Sultanov, V.B.: Possibility of a (bi) polaron high-temperature superconductivity in Poly A/Poly T DNA duplexes. J. Appl. Phys. 112(6), 064701 (2012)
Landau, L.: On the properties of metals at very low temperatures. Phys. Z. Sowjetunion 3(4), 545 (1933)
McQueeney, R..J., Petrov, Y., Egami, T., Yethiraj, M., Shirane, G., Endoh, Y.: Anomalous dispersion of LO phonons in La\(_{1.85}\) at low temperatures. Phy. Rev. Lett. 82(3), 628 (1999)
Nekorkin, V., Velarde, M.G.: Synergetic Phenomena in Active Lattices: Patterns, Waves, Solitons, Chaos. Springer, Berlin (2002)
Pekar, S.I.: Untersuchungen über die Elektronentheorie der Kristalle. Akademie-Verlag, Berlin (1954)
Rashba, E.: Absorption of light by crystals. Izv. Acad. Nauk USSR, Ser. Fiz. 21, 37 (1957)
Remoissenet, M.: Waves Called Solitons: Concepts and Experiments. Springer Science & Business Media, Berlin (1999)
Russell, F.M., Collins, D.R.: Lattice-solitons and non-linear phenomena in track formation. Radiat. Meas. 25(1), 67–70 (1995)
Scott, A.: Davydov’s soliton. Phys. Rep. 217(1), 1–67 (1992)
Scott, A., Christiansen, P.L. (eds.): Davydov’s Soliton Revisited: Self-trapping of Vibrational Energy in Protein. Springer, New York (1991)
Streetman, B.G., Banerjee, S.: Solid State Electronic Devices, vol. 4. Prentice Hall, Upper Saddle River, NJ (2000)
Toda, M.: Theory of Nonlinear Lattices, 2nd edn. Springer-Verlag, Berlin (1989)
Toda, M.: Nonlinear Waves and Solitons, KTK Scientific Publishers, Tokyo (1989)
Velarde, M.G.: From polaron to solectron: the addition of nonlinear elasticity to quantum mechanics and its possible effect upon electric transport. J. Comp. Appl. Math. 233(6), 1432–1445 (2010)
Velarde, M.G., Brizhik, L., Chetverikov, A.P., Cruzeiro, L., Ebeling, W., Röpke, G.: Electron pairing in one-dimensional anharmonic crystal lattices. Int. J. Quantum Chem. 112(2), 551–565 (2012)
Velarde, M.G., Brizhik, L., Chetverikov, A.P., Cruzeiro, L., Ebeling, W., Röpke, G.: Quartic lattice interactions, soliton-like excitations, and electron pairing in one-dimensional anharmonic crystals. Int. J. Quantum Chem. 112(13), 2591–2598 (2012)
Velarde, M.G., Ebeling, W., Chetverikov, A.P.: Thermal solitons and solectrons in 1D anharmonic lattices up to physiological temperatures. Int. J. Bifurcat. Chaos 18(12), 3815–3823 (2008)
Velarde, M.G., Neißner, C.: Soliton-mediated electron pairing. Int. J. Bifurcat. Chaos 18(03), 885–890 (2008)
Wilson, E.G.: A new theory of acoustic solitary-wave polaron motion. J. Phys. C Solid State 16(35), 6739 (1983)
Ying, Y.A., Nelson, K.D., Deac, I.G., Schiffer, P., Khalifah, P., Cava, R.J., Liu, Y.: Possible observation of quantum ferromagnetic fluctuations in La\(_4\). Phys. Rev. B 80(2), 024303 (2009)
Zolotaryuk, A.V., Spatschek, K.H., Savin, A.V.: Supersonic mechanisms for charge and energy transfers in anharmonic molecular chains. Phys. Rev. B 54(1), 266 (1996)
Acknowledgments
The authors acknowledge fruitful discussions and correspondence with A.S. Alexandrov (deceased), V.S. Anishchenko, A. Bussmann-Holder, L.A. Cisneros-Ake, L. Cruzeiro, S. Dmitriev, K. Donovan, C. Ford, D. Hennig, J.P. Launay, R.P.G. McNeil, T. Meunier, V.I. Nayanov, D.M. Newns, G. Röpke, F.M. Russell, E.G. Wilson and A. Wixforth. This research was partly supported by the Spanish Ministerio de Economia y Competitividad under grant MAT2011-26221. L. Brizhik acknowledges partial support from the Fundamental Research Grant of the National Academy of Sciences of Ukraine.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Brizhik, L.S., Chetverikov, A.P., Ebeling, W., Röpke, G., Velarde, M.G. (2015). Bound States of Electrons in Harmonic and Anharmonic Crystal Lattices. In: Archilla, J., Jiménez, N., Sánchez-Morcillo, V., García-Raffi, L. (eds) Quodons in Mica. Springer Series in Materials Science, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-21045-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-21045-2_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21044-5
Online ISBN: 978-3-319-21045-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)