Anomalous electron diffusion in fractal systems at low temperatures

Abstract

Experimental studies of electron diffusion on statistical as well as deterministic fractals are represented and discussed. Especially, thin gold films close to the percolation threshold and Sierpinski gaskets made of Al wires are considered. As theoretically predicted (electron) diffusion becomes length dependent (anomalous diffusion) for diffusion lengths R smaller than a distinct length ξp, below which the system is self-similar. For diffusion lengths R larger than ξp the diffusion process is length independent (normal diffusion). It is shown that for percolating (gold) films the phase coherence length Lϕ plays the role of a diffusion length exhibiting normal (LO > ξp) and anomalous electron diffusion (LO < ξp). From the temperature dependence of Lϕ(T) one obtains the fractal dimension for random walks which well agrees with theoretical predictions. For Sierpinski gaskets the superconducting correlation length ξs is the suitable length probing anomalous diffusion. Since ξs is linked to the upper critical field Hc2 of the superconducting network studying the phase boundary behavior yields the critical exponents for anomalous diffusion on Sierpinski gaskets.