Small Polarons in Dense Lattice Systems

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 x0. 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 ħω0. (Here u=(x20/2x2zp) with xzp being the zero point phonon displacement.) The relevance of these results for CMR oxides is briefly discussed.