Some finite temperature aspects of the Anderson transition

The conductivity versus temperature, sigma (T) of disordered, three-dimensional indium oxide samples is analysed. It is demonstrated that the temperature dependence of sigma (T) as a function of disorder is in semi-quantitative agreement with current theories of the Anderson transition. In particular, it is shown that Imry's scale-dependent-diffusion regime exists over a well defined range of disorder. It is pointed out that at finite temperatures, insulating samples may appear to be conducting. This happens above a characteristic, disorder dependent temperature. It is also demonstrated that the situation is qualitatively different in a disordered two-dimensional system. A conjecture is then raised that the excess conductivity observed at high temperatures in three-dimensional systems reflects high-mobility states above a threshold energy. This conjecture is shown to be consistent with several hitherto unexplained experimental observations.