Breather-induced anomalous charge diffusion.

We present results on the diffusive motion of a charge interacting with the nonlinear dynamics of a thermalized underlying lattice. Signatures of anomalous diffusive properties are found at relatively high temperatures, where highly nonlinear excitations are present. A sublinear diffusion and a plateau appear before the standard long-time diffusion during the evolution of the mean-squared displacement and a significant degree of heterogeneity is exhibited among individual trajectories. Both properties are connected with the existence of vibrational hot spots (breather or multibreather excitations). Transport parameters of the charge are strongly affected in this case, as can be exemplified by the significant suppression of the diffusion coefficient D. The variation of D with temperature follows a stretched exponential law. The results are contrasted with those of the linearized case, in the absence of breathers. Such anomalous diffusion of a charge coupled to a thermalized lattice may be relevant in low-dimensional soft materials with strong anharmonicities, such as biomolecules, conducting polymers, etc.