Evidence for superlocalization on a fractal network in conductive carbon-black–polymer composites

Abstract

The dc conductivity of carbon-black--polymer composites has been measured as a function of carbon-black concentration from just above the percolation threshold ${\mathit{p}}_{\mathit{c}}$ up to 33${\mathit{p}}_{\mathit{c}}$, and in the temperature range from 4 to 300 K. To explain the temperature dependence we have modified the Mott-Deutscher model for variable-range hopping between superlocalized states on a fractal by assuming Coulomb-dominated hopping. Our data then yield the first experimental evidence of electron superlocalization, with a superlocalization exponent \ensuremath{\zeta}=1.94\ifmmode\pm\else\textpm\fi{}0.06, close to theoretical estimates. The derived localization length is of the right order of magnitude.