Lattice Polarons and Switching in Molecular Nanowires and Quantum Dots

  • A. S. Alexandrov
Part of the Nanostructure Science and Technology book series (NST)


Conducting electrons in inorganic and organic matter interact with vibrating ions. If phonon frequencies are sufficiently low, the local deformation of ions, caused by the electron itself, creates a potential well, which traps the electron even in a perfect crystal lattice. This self-trapping phenomenon was predicted by Landau [1]. It was studied in greater detail by Pekar [2], Fröhlich [3], Feynman [4], Rashba [5], Devreese [6], and other authors in the effective mass approximation for the electron placed in a continuous polarizible medium, which leads to a so-called large or continuous polaron. Large-polaron wave functions and corresponding lattice distortions spread over many lattice constants (see Fig. 8.1). The trapping is never complete in the perfect lattice. Due to finite phonon frequencies, ion polarizations follow polaron motion if the motion is sufficiently slow. Hence, large polarons with a low kinetic energy propagate through the lattice as free electrons but with an enhanced effective mass.

An electron shifts the equilibrium position of Na+ and Cl ions in the ionic lattice of and forms a large (or intermediatej-radius polaron.


Coulomb Repulsion Small Polaron Quantum Monte Carlo Effective Mass Approximation Large Polaron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    L.D. Landau, Physikalische Zeitschrift der Sowjetunion 3, 664 (1933).Google Scholar
  2. 2.
    S.I. Pekar, Autolocalization of the electron in a dielectric inertially polarizing medium, Zh. Eksp. Teor. Fiz. 16, 335 (1946).Google Scholar
  3. 3.
    H. Froehlich, Electrons in lattice fields, Adv. Phys. 3, 325 (1954).CrossRefGoogle Scholar
  4. 4.
    R.P. Feynman, Slow electrons in a polar crystal, Phys. Rev. 97, 660 (1955).CrossRefGoogle Scholar
  5. 5.
    E.I. Rashba, Theory of strong interactions of electron excitations with lattice vibrations in molecular crystals, Optika i spektroskopia 2, 75 (1957).Google Scholar
  6. 6.
    J.T. Devreese, Polarons in Encyclopedia of Applied Physics, vol. 14, VCH New York, 1996, p. 383.Google Scholar
  7. 7.
    S.V. Tyablikov, Electron energy spectrum in a polar crystal, Zh. Eksp. Teor. Fiz. 23, 381 (1952).Google Scholar
  8. 8.
    J. Yamashita and T. Kurosawa, On electronic current in NiO, J. Phys. Chem. Solids 5, 34 (1958).CrossRefGoogle Scholar
  9. 9.
    G.L. Sewell, Electrons in polar crystals, Phil. Mag. 3, 1361 (1958).CrossRefGoogle Scholar
  10. 10.
    T. Holstein, Studies of polaron motion, Ann. Phys. 8, 325, 343 (1959); L. Friedman and T. Holstein, Studies of polaron motion 3: the hall mobility of the small polaron, Ann. Phys. 21 494 (1963); D. Emin and T. Holstein, Studies of small-polaron motion 4: adiabatic theory of hall effect, Ann. Phys. 53, 439 (1969).CrossRefGoogle Scholar
  11. 11.
    I.G. Lang and Yu. A. Firsov, Kinetic theory of semiconductors with low mobility, Sov. Phys. JETP 16, 1301 (1963).Google Scholar
  12. 12.
    D.M. Eagles, Optical absorption in ionic crystals involving small polarons, optical absorption in ionic crystals involving small polarons, Phys. Rev. 130, 1381 (1963).CrossRefGoogle Scholar
  13. 13.
    Yu.A. Firsov (ed.) Polarons, (Moscow: Nauka), 1975; H. Boettger and V.V. Bryksin, Hopping Conduction in Solids, Academie-Verlag, Berlin, 1985; A.M. Stoneham, Small polarons and polaron transitions, J. Chem. Soc. Faraday II 85, 505 (1989); G.D. Mahan, Many Particle Physics, Plenum, New York, 1990; A.L. Shluger and A.M. Stoneham, Small polarons in real crystals—concepts and problems, J. Phys. Condens. Matter 1, 3049 (1993); A.S. Alexandrov and N.F. Mott, Polarons and Bipolarons, World Scientific, Singapore, 1995; N. Itoh and A.M. Stoneham, Materials Modification by Electronic Excitation Cambridge University Press, Cambridge, 2001.Google Scholar
  14. 14.
    V.L. Vinetskii and M.S. Giterman, On the theory of the interaction of excess charges in ionic crystals, Sov. Phys. JETP 6, 560 (1958).Google Scholar
  15. 15.
    S.G. Suprun and B.Y. Moizhes, Electron correlation effect in pekar bipolaron formation, Sov. Phys. Solid State 24, 903 (1982).Google Scholar
  16. 16.
    J. Adamowski, Formation of frohlich bipolarons, hys. Rev. B 39, 3649 (1989).CrossRefGoogle Scholar
  17. 17.
    F. Bassani, M. Geddo, G. Iadonisi, and D. Ninno, Variational calculations of bipolaron binding-energies, Phys. Rev. 543, 5296 (1991).Google Scholar
  18. 18.
    G. Verbist, F.M. Peters, and J.T. Devreese, Large bipolarons in 2 and 3 dimensions, Phys. Rev. B 43, 2712 (1991).CrossRefGoogle Scholar
  19. 19.
    K.A. Müller, Jahn-Teller bipolarons and their condensation, Physica Scripta T 102 39 (2002), and references therein.CrossRefGoogle Scholar
  20. 20.
    A.S. Alexandrov, Bipolaron anisotropic flat bands, Hall mobility edge, and metal-semiconductor duality of overdoped high-T-c oxides, Phys. Rev. B 53, 2863 (1996).CrossRefGoogle Scholar
  21. 21.
    P.W. Anderson, Model for electronic-structure of amorphous-semiconductors, Phys. Rev. Lett. 34, 953 (1975); R.A. Street and N.F. Mott, States in gap in glassy semiconductors, Phys. Rev. Lett. 35, 1293 (1975).CrossRefGoogle Scholar
  22. 22.
    B.K. Chakraverty, Possibility of insulator to superconductor phase-transition, J. Phys. Lett. (Paris) 40, L–99, (1979).Google Scholar
  23. 23.
    A.S. Alexandrov and J. Ranninger, Theory of bipolarons and bipolaronic bands, Phys. Rev. B 23, 1796 (1981); A.S. Aleksandrov (Alexandrov), Bipolarons in narrow-zone crystals, Russ. J. Phys. Chem. 57, 167 (1983).CrossRefGoogle Scholar
  24. 24.
    S. Aubry, High-Tc superconductivity with polarons and bipolarons: an approach from the insulating state, in Polarons and Bipolarons in High-Tc Superconductors and Related Materials, edited by E.K.H. Salje, A.S. Alexandrov, and W.Y. Liang, Cambridge University Press, Cambridge, 1995, p. 271; A.R. Bishop and M. Salkola, Polarons in Peierls-Hubbard models, in Polarons and Bipolarons in High-Tc Superconductors and Related Materials, edited by E.K.H. Salje, A.S. Alexandrov, and W.Y. Liang, Cambridge University Press, Cambridge, 1995, p. 353.CrossRefGoogle Scholar
  25. 25.
    F. Marsiglio, Pairing in the holstein model in the dilute limit, Physica C 244, 21 (1995).CrossRefGoogle Scholar
  26. 26.
    Y. Takada and T. Higuchi, Vertex function for the coupling of an electron with intramolecular phonons—exact results in the antiadiabatic limit, Phys. Rev. B 52 12720 (1995).CrossRefGoogle Scholar
  27. 27.
    A.J. Millis, P.B. Littlewood, and B.I. Shraiman, Double exchange alone does not explain the resistivity of Lal-xSrxMnO3, Phys. Rev. Lett. 74, 5144 (1995).CrossRefGoogle Scholar
  28. 28.
    C. Baesens C and R. S. MacKay, Finite coherence length for equilibrium states of generalized adiabatic Holstein models, J. Math. Phys. 38, 2104 (1997).CrossRefGoogle Scholar
  29. 29.
    H. Fehske, J. Loos, and G. Wellein, Spectral properties of the 2D Holstein polaron, Z. Phys. B 104, 619 (1997).CrossRefGoogle Scholar
  30. 30.
    A.S. Alexandrov, Theory of superconductivity: from weak to strong coupling, IoP Publishing, Bristol, 2003.Google Scholar
  31. 31.
    T. Gerisch, R. Münzner, and A. Rieckers, Canonical versus grand-canonical free energies and phase diagrams of a bipolaronic superconductor model, J. Statisti. Phys. 93, 1021 (1998).CrossRefGoogle Scholar
  32. 32.
    T. Frank and M. Wagner, Contrasting unitary transformations for the standard bipolaron model, Phys. Rev. B 60, 3252 (1999).CrossRefGoogle Scholar
  33. 33.
    P. Benedetti and R. Zeyher, Holstein model in infinite dimensions at half-filling, Phys. Rev. B 58, 14320 (1998).CrossRefGoogle Scholar
  34. 34.
    A.S. Alexandrov, V.V. Kabanov, and D.K. Ray, From electron to small polaron—an exact cluster solution, Phys. Rev. B 49, 9915 (1994).CrossRefGoogle Scholar
  35. 35.
    H. Fehske, J. Loos, and G. Wellein, Spectral properties of the 2D Holstein polaron, Zeitschrift furPhysikB: Cond. Mat. 104, 619 (1997).CrossRefGoogle Scholar
  36. 36.
    A.H. Romero, D.W. Brown, and K. Lindenberg, Converging toward a practical solution of the Holstein molecular crystal model, J. Chem. Phys. 109, 6504 (1998).CrossRefGoogle Scholar
  37. 37.
    A. LaMagna and R. Pucci, Variational study of the discrete Holstein model, Phys. Rev. B 53, 8449 (1996).CrossRefGoogle Scholar
  38. 38.
    J. Bonca, S.A. Trugman, and I. Batistic, Holstein polaron, Phys. Rev. 560, 1633 (1999).Google Scholar
  39. 39.
    L. Proville and S. Aubry, Small bipolarons in the 2-dimensional Holstein-Hubbard model:The adiabatic limit, Eur. Phys. J. B 11, 41 (1999).CrossRefGoogle Scholar
  40. 40.
    S.A. Trugman, J. Bonca, and L.C. Ku, Statics and dynamics of coupled electron-phonon systems, Int. J. Mod. Phys. B 15, 2707 (2001), and references therein.CrossRefGoogle Scholar
  41. 41.
    P.E. Kornilovitch, Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron, Phys. Rev. Lett. 81, 5382 (1998).CrossRefGoogle Scholar
  42. 42.
    N.V. Prokof’ev and B.N. Svistunov, Polaron Problem by Diagrammatic Quantum Monte Carlo, Phys. Rev. Lett. 81, 2514 (1998).CrossRefGoogle Scholar
  43. 43.
    J.M. Lehn, Perspectives in supramolecular chemistry—from molecular recognition towards molecular information-processing and self-organization, Angew. Chem. Int. Ed. Engl. 29, 1304 (1990).CrossRefGoogle Scholar
  44. 44.
    J.M. Tour, Molecular electronics: Synthesis and testing of components, Ace. Chem. Res. 33, 791 (2000).CrossRefGoogle Scholar
  45. 45.
    A. Aviram and M. Ratner (eds.), Molecular Electronics: Science and Technology, New York Academy of Science, New York, 1998.Google Scholar
  46. 46.
    C.P. Collier, E.W. Wong, M. Belohradsky, F.M. Raymo, J.F. Stoddart, P.J. Kuekes, R.S. Williams, and J.R. Heath, Electronically configurable molecular-based logic gates, Science 285, 391 (1999); D.I. Gittins, D. Bethell, DJ. Schiffrin, and R.J. Nichols, A nanometre-scale electronic switch consisting of a metal cluster and redox-addressable groups, Nature (London) 408, 67 (2000).CrossRefGoogle Scholar
  47. 47.
    N.B. Zhitenev, H. Meng, and Z. Bao, Conductance of small molecular junctions, Phys. Rev. Lett. 88, 226801 (2002).CrossRefGoogle Scholar
  48. 48.
    J. Park, A.N. Pasupathy, J.I. Goldsmith, C. Chang, Y. Yaish, J.R. Retta, M. Rinkoski, J.P. Sethna, H.D. Abruña, P.L. McEuen, and D.C. Ralph, Coulomb blockade and the Kondo effect in single-atom transistors, Nature (London) 417 722 (2002).CrossRefGoogle Scholar
  49. 49.
    L.I. Glazman and R.I. Shekhter, Inelastic resonance tunneling of electrons through a potential barrier, Zh. Eksp. Teor. Fiz. 94, 292 (1987); N.S. Wingreen, K.W. Jacobsen, and J.W. Wilkins, Inelastic-scattering in resonant tunneling, Phys. Rev. B 40, 11834 (1989).Google Scholar
  50. 50.
    Xi Li, Hao Chen, and Shi-xun Zhou, Conductance of a quantum dot with a Hubbard inter action in the presence of a boson field, Phys. Rev. B 52, 12202 (1995).CrossRefGoogle Scholar
  51. 51.
    K. Kang, Transport through an interacting quantum dot coupled to two superconducting leads, Phys. Rev. B 57, 11891 (1998).CrossRefGoogle Scholar
  52. 52.
    V.N. Ermakov, Resonant electron tunneling through double-degenerate local state with account of strong electron-phonon interaction, Physica E 8, 99 (2000).CrossRefGoogle Scholar
  53. 53.
    M. Di Ventral, S.-G. Kim, S. T. Pantelides, and N.D. Lang, Temperature Effects on the Transport Properties of Molecules, Phys. Rev. Lett. 86, 288 (2001).CrossRefGoogle Scholar
  54. 54.
    N. Ness, S.A. Shevlin, and A.J. Fisher, Coherent electron-phonon coupling and polaronlike transport in molecular wires, Phys. Rev. B 63, 125422 (2001).CrossRefGoogle Scholar
  55. 55.
    U. Lundin and R.H. McKenzie, Temperature dependence of polaronic transport through single molecules and quantum dots, Phys. Rev. B 66, 075303 (2002).CrossRefGoogle Scholar
  56. 56.
    A.S. Alexandrov, I.K. Yanson, and J. Demsar (eds.), Molecular Nanowires and Other Quantum Objects, Kluwer Academic, Amsterdam, 2004.Google Scholar
  57. 57.
    A.S. Alexandrov, A.M. Bratkovsky, and R.S. Williams, Bistable tunneling current through a molecular quantum dot, Phys. Rev. B 67, 075301 (2003).CrossRefGoogle Scholar
  58. 58.
    D. Stewart, Y. Chen, and R.S. Williams, unpublished data.Google Scholar
  59. 59.
    A.S. Alexandrov and A.M. Bratkovsky, Memory effect in a molecular quantum dot with strong electron-vibron interaction, Phys. Rev. B 67, 235312 (2003).CrossRefGoogle Scholar
  60. 60.
    A.S. Alexandrov and P.E. Kornilovich, Mobile Small Polaron, Phys. Rev. Lett. 82, 807 (1999).CrossRefGoogle Scholar
  61. 61.
    A.S. Alexandrov and P.E. Kornilovitch, The Frohlich-Coulomb model of high-temperature superconductivity and charge segregation in the cuprates, J. Phys.: Condens. Matter 14, 5337 (2002).CrossRefGoogle Scholar
  62. 62.
    N.S. Wingreen and Y. Meir, Anderson model out of equilibrium: Noncrossing-approximation approach to transport through a quantum dot, Phys. Rev. B 49, 11040 (1994) and references therein.CrossRefGoogle Scholar
  63. 63.
    W.P. Su and J.R. Schrieffer, Soliton dynamics in polyacetylene, Proc. Natl. Acad. Sci. 77, 5626 (1980).CrossRefGoogle Scholar
  64. 64.
    A. Feldblum, J.H. Kaufman, S. Etemad, and A.J. Heeger, Opto-electrochemical spectroscopy of trans-(CH)x, Phys. Rev. B 26, 815 (1982).CrossRefGoogle Scholar
  65. 65.
    R.R. Chance, J.L. Bredas, and R. Silbey, Bipolaron transport in doped conjugated polymers, Phys. Rev. B 29, 4491 (1984).CrossRefGoogle Scholar
  66. 66.
    M.G. Ramsey, D. Steinmuller, and F.P. Netzer, Explicit evidence for bipolaron formation: Cs-doped biphenyl, Phys. Rev. B 42, 5902 (1990).CrossRefGoogle Scholar
  67. 67.
    D. Steinmuller, M.G. Ramsey, and F.P. Netzer, Polaron and bipolaronlike states in n-doped bithiophene, Phys. Rev. B 47, 13323 (1993).CrossRefGoogle Scholar
  68. 68.
    L.S. Swanson, J. Shinar, A.R. Brown, D.D.C. Bradley, R.H. Friend, P.L. Burn, A. Kraft, and A.B. Holmes, Electroluminescence-detected, conductivity-detected, and photoconductivity-detected magnetic-resonance study of poly(p-phenylenevinylene)-based light-emitting-diodes, Synth. Metals 55, 241 (1993).CrossRefGoogle Scholar
  69. 69.
    A.S. Alexandrov, A.M. Bratkovsky, and P.E. Kornilovitch, Two-electron elastic tunneling in low-dimensional conductors, Phys. Rev. B 65, 155209 (2002).CrossRefGoogle Scholar
  70. 70.
    Y. Meir and N.S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett. 68, 2512 (1992).CrossRefGoogle Scholar
  71. 71.
    R. Micnas, J. Ranninger, and S. Robaszkiewicz, Superconductivity in narrow-band systems with local nonretarded attractive interactions, Rev. Mod. Phys. 62, 113 (1990), and references therein.CrossRefGoogle Scholar
  72. 72.
    A.S. Alexandrov and V.V. Kabanov, Theory of superconducting Tc of doped fullerenes, Phys. Rev. B 54, 3655 (1996).CrossRefGoogle Scholar
  73. 73.
    A.S. Alexandrov and A.M. Bratkovsky, The essential interactions in oxides and spectral weight transfer in doped manganites, Z. Phys.-Condens. Mat. 11, L531 (1999).CrossRefGoogle Scholar
  74. 74.
    J.R. Heath, J.F. Stoddart, and R.S. Williams, More on molecular electronics, Science 303, 1136 (2004).CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • A. S. Alexandrov
    • 1
  1. 1.Department of PhysicsLoughborough UniversityLoughboroughUK

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