Abstract
There is considerable evidence for the persistence of small polaron like entities in colossal magnetoresistance oxides, which are dense electronic systems with electron density n≲1 per site. This has brought up again the question of whether and how small (narrow band) polaronic states survive in a dense electronic system. We investigate this question in a simple one band Holstein polaron model, in which spinless electrons on a tight binding lattice cause an on-site lattice distortion x 0 . In the small polaron limit, each electron is localized, and the electron hopping tij is neglected. We develop a systematic approach in powers of tij, identify classical t0, quantum mean field t1, and quantum fluctuation t2 terms, and show that the last two terms are relatively small, even for dense systems, so long as the narrowed polaron bandwidth t*=t exp(−u) is much smaller than the Einstein phonon energy ħω 0 . (Here u=(x2 0 /2x2 zp) with xzp being the zero point phonon displacement.) The relevance of these results for CMR oxides is briefly discussed.
Similar content being viewed by others
REFERENCES
Some review articles and books describing phenomena in this expanding field are the following: E. Dagotto, T. Hotta, and A. Moreo, Phys. Rep. 344, 1 (2001). J. M. D. Coey, M. Viret, and S. von Molnar, Adv. in Phys. 48, 167 (1999). Colossal Magnetoresistance, Charge Ordering and Related Properties of Manganese Oxides ( eds. C. N. R. Rao and B. Raveau, World Scientific, Singapore, 1998). Colossal Magnetoresistance Oxides (ed. Y. Tokura, Gordon and Breach, London, 1999).
G.-M Zhao et al., cond-mat/9912355.
G.-M. Zhao, K. Conder, H. Keller, and K. A. Müller, Nature 381, 676 (1996).
A. Anane et al., J. Phys.: Condensed Matter 7, 7015 (1995).
R. H. Heffner et al., Phys. Rev. Lett. 85, 3285 (2000).
M. Fäth, S. Freisem, A. A. Menovsky, Y. Tomioka, J. Aarts, and J. A. Mydosh, Science 285, 1540 (1999).
M. Uehara, S. Mori, C. H. Chen, and S.-W. Cheong, Nature 399, 560 (1999).
H. Röder, J. Zang, and A. R. Bishop, Phys. Rev. Lett. 76, 1356 (1996).
A. S. Alexandrov and P. E. Kornilovitch, Phys. Rev. Lett. 82, 807 (1999).
A. S. Alexandrov and A. M. Bratkovsky, Phys. Rev. Lett. 82, 141 (1999).
A. J. Millis, B. Shraiman, and R. Mueller, Phys. Rev. B 54, 5405 (1996); U. Yu and B. I. Min, cond-mat/9906263.
Further details are given in G. Venketeswara Pai and T. V. Ramakrishnan, to be published.
G. Venketeswara Pai and T. V. Ramakrishnan, to be published.
See for example, T. Holstein, Ann. Phys. 8, 325 (1959); ibid. 8, 343 (1959).
I. G. Lang and Yu. A. Firsov, Sov. Phys.-Solid State 5, 2049 (1964).
P. Gosar, J. Phys. C: Solid State 8, 3584 (1975). See also Y. Toyozawa, Prog. Theor. Phys. 26, 29 (1961).
V. Cataudella, G. De Filippis, and G. Iadonisi, Phys. Rev. B 60, 15163 (1999).
A. H. Romero, D. W. Brown, and K. Lindenberg, Phys. Rev. B 59, 13728 (1999).
A. A. Gogolin, Phys. Status Solidi B 109, 95 (1982).
K. H. Ahn and A. J. Millis, Phys. Rev. B 61, 13545 (2000); ibid. 64, 115103 (2001).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ramakrishnan, T.V., Pai, G.V. Small Polarons in Dense Lattice Systems. Journal of Low Temperature Physics 126, 1055–1065 (2002). https://doi.org/10.1023/A:1013859028130
Issue Date:
DOI: https://doi.org/10.1023/A:1013859028130