Formal analogy between anomalous dispersive transport and dispersion in polarization processes. A physical interpretation of the Cole and Cole formula

Measurements of transient polarization in insulators can often be explained on the basis of a complex dielectric constant taking the form proposed by Cole and Cole. The latter, which indeed leads to a power-law decaying absorption current, consists in correcting the simple Debye expression to account for some dispersion in the time required to line-up dipoles in a dielectric submitted to a voltage step. Despite of its success, the Cole and Cole formula has not received any convincing physical explanation. It introduces dispersion from a mathematical trick and is not based on a particular description of the polarization at the microscopic scale. The physical reasons for the dispersion are therefore obscure. Carrier transport is another field where dispersion occurs. In this case however, numerous published works have contributed to draw some clear physical pictures for it, the most successful models involving hopping and multiple-trapping in presence of an exponential distribution of trapping levels. This work shows that the Cole and Cole formalism is formally equivalent to the standard multiple-trapping model of dispersive transport. This similarity allows us to propose a physical mechanism for dispersive polarization which explains the Cole and Cole formula.