Vibrational Dispersion and Small-Polaron Motion: Enhanced Diffusion

The one-dimensional molecular-crystal model of Holstein is utilized in a preliminary investigation of the effects of the dispersion of the longitudinal optical frequencies on the hopping motion of small polarons. In particular, this work raises the question of whether the lattice relaxes sufficiently rapidly after a small-polaron hop so that a subsequent hop of the excess carrier may be considered independent of the initial hop. To this end, Holstein's perturbative approach is applied in calculating the probability of an initial small-polaron jump being followed by another small-polaron hop at a time $t$ later. Furthermore, the small-polaron drift mobility is calculated assuming that the polaron's jump rate is only influenced by its immediately preceding hop. It is found that, for the circumstance in which the average time between jumps is small compared with the relaxation time of the lattice, the activation energy characterizing the small-polaron drift mobility is smaller than that found for completely independent jumps. In fact, for appropriate choices of the physical parameters, the drift mobility may display a very mild temperature dependence, decreasing with increasing temperature at sufficiently high temperatures.