Coulomb zero bias anomaly for fractal geometry and conductivity of granular systems near the percolation threshold

摘要

A granular system slightly below the percolation threshold is a collection offinite metallic clusters, characterized by wide spectrum of sizes, resistances,and charging energies. Electrons hop from cluster to clusters via shortinsulating "links" of high resistance. At low temperatures all clusters areCoulomb blockaded and the dc-conductivity is exponentially suppressed. Atlowest T the leading transport mechanism is variable range cotunneling vialargest (critical) clusters, leading to the modified Efros-Shklovsky law. Atintermediate temperatures the principal suppression of the conductivityoriginates from the Coulomb zero bias anomaly occurring, when electron tunnelsbetween adjacent large clusters with large resistances. Such clusters areessentially extended objects and their internal dynamics should be taken intoaccount. In this regime the T-dependence of conductivity is stretchedexponential with a nontrivial index, expressed through the indices ofpercolation theory. Due to the fractal structure of large clusters the anomalyis strongly enhanced: it arises not only in low dimensions, but also in d=3case.