Ageing and relaxation times in disordered insulators

We focus on the slow relaxations observed in the conductance of disordered insulators at low temperature (especially granular aluminum films). They manifest themselves as a temporal logarithmic decrease of the conductance after a quench from high temperatures and the concomitant appearance of a field effect anomaly centered on the gate voltage maintained. We are first interested in ageing effects, i.e. the age dependence of the dynamical properties of the system. We stress that the formation of a second field effect anomaly at a different gate voltage is not a 'history free' logarithmic (lnt) process, but departs from lnt in a way which encodes the system's age. The apparent relaxation time distribution extracted from the observed relaxations is thus not 'constant' but evolves with time. We discuss what defines the age of the system and what external perturbation out of equilibrium does or does not rejuvenate it. We further discuss the problem of relaxation times and comment on the commonly used 'two dip' experimental protocol aimed at extracting 'characteristic times' for the glassy systems (granular aluminum, doped indium oxide...). We show that it is inoperable for systems like granular Al and probably highly doped InOx where it provides a trivial value only determined by the experimental protocol. But in cases where different values are obtained like in lightly doped InOx or some ultra thin metal films, potentially interesting information can be obtained, possibly about the 'short time' dynamics of the different systems. Present ideas about the effect of doping on the glassiness of disordered insulators may also have to be reconsidered.