Coulomb zero bias anomaly for fractal geometry and conductivity of granular systems near the percolation threshold
A. S. Ioselevich
Landau Institute for Theoretical Physics RAS, 117940 Moscow, Russia
Moscow Institute of Physics and Technology, 141700 Moscow, Russia
A granular system
slightly below the percolation
threshold is a collection of finite metallic
clusters, characterized by wide spectrum of sizes, resistances,
and charging energies. Electrons hop from cluster to clusters via
short insulating «links» of high resistance.
At low temperatures all clusters are Coulomb blockaded and the
dc-conductivity σ is exponentially suppressed.
At lowest T the leading transport mechanism is
variable range cotunneling via largest (critical) clusters,
leading to the modified Efros-Shklovsky law.
At intermediate temperatures the principal
suppression of σ originates from the Coulomb zero bias
anomaly occurring, when electron tunnels between adjacent large
clusters with large resistances. Such clusters are essentially
extended objects and their internal dynamics should be taken
into account. In this regime the T-dependence of σ is
stretched exponential with a nontrivial index, expressed
through the indices of percolation theory. Due to the fractal
structure of large clusters the
anomaly is strongly enhanced: it arises
not only in low dimensions, but also in d=3 case.