Hopping dynamics of interacting polarons

We derive an effective cluster model to address the transport properties of mutually interacting small polarons. We propose a decoupling scheme where the hopping dynamics of any given particle is determined by separating out explicitly the degrees of freedom of its environment, which are treated as a statistical bath. The general cavity method developed here shows that the long-range Coulomb repulsion between the carriers leads to a net increase of the thermal activation barrier for electrical transport, and hence to a sizable reduction of the carrier mobility. A mean-field calculation of this effect is provided, based on the known correlation functions of the interacting liquid in two and three dimensions. The present theory gives a natural explanation of recent experiments performed in organic field-effect transistors with highly polarizable gate dielectrics, and might well find application in other classes of polaronic systems such as doped transition-metal oxides.