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 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 t 0 , quantum mean field t^ 1 , and quantum fluctuation t^ 2 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 h(omega)0 . (Here u=(x ^2 0 /2x^ 2 zp) with xzp being the zero point phonon displacement.) The relevance of these results for CMR oxides is briefly discussed.