<title>Conduction in nanocomposites: hopping on a fractal</title>

Abstract

We discuss the mechanism of hopping conduction in nanocomposites and similar materials where the size of hopping sites is large compared to edge-to-edge separations between the sites. In this case the dominant mechanism involving transitions via virtual intermediate localized states is characterized by the increase in tunneling probabilities between distant sites; moreover the coherent tunneling path via virtual intermediate states is restricted to the fractal incipient percolation cluster. The application of percolation arguments to the calculation of the system conductivity is based on the concept of the generalized chemical distance. The resulting d.c. conductivity temperature dependence is of the form ln&sigma; approximately -(<i>T</i>_o/<i>T</i>)^x, where the exponent x is expressed in terms of the critical exponent for the chemical distance (or superlocalization exponent) and fractal dimensionality of the backbone cluster.