Transition from the metallic into the localized phase: the conductance distribution

We study numerically the changes of the conductance distribution P (g) caused by the transition of the system from the metallic into the insulating regime. Two different scenarios of the transition are discussed and compared: (i) localization in the weakly disordered quasi-one dimensional systems and (ii) disorder-induced localization. Transition from the metallic into the localized regime is an evergreen theme in the studies of the electronic transport in disordered systems. While the weak disorder limit is well understood and described in the framework of the random matrix theory (RMT) [1] and the DMPK equation [2], no equivalent theoretical description of the strongly disordered limit exists. Even less is known about the intermediate regime. The last one is of special interest for it includes also a critical regime of the metal-insulator transition. Owing to the absence of self-averaging of the conductance in disordered systems at zero temperature [3], an understanding of statistical transport properties requires the knowledge of the whole conductance distribution P (g). P (g) is well known in the limiting regimes: in the weakly disordered metallic regime, RMT as well as the analysis of the DMPK equation predict that P (g) is Gaussian with constant, disorder independent width. This prediction has been numerically verified for Q1D, square and cubic samples [1, 4, 5]. In the opposite limit of strong localization the distribution of log g is Gaussian with var log g = −const× log g and const = 2 for Q1D and 1 for squares (cubes) [1]. The transformation of the conductance distribution from the normal to log-normal form due to the transition of the system from the metallic into localized regime has not yet been completely understood. Our aim in this work is to present numerical data for the conductance distribution in the intermediate regime between the metallic and the localized phases. We discuss two different scenarios for the transition into the localized regime, the first governed by changes of the system shape and the second one by increase of the disorder. We analyze the origin of differences between conductance distribution in these scenarios.