Anderson localization in quantum high magnetic field

Abstract

1. I N T R O D U C T I O N New interest to investigations of transverse and longitudinal diffusion in quantum high magnetic field H is connected with a progress in understanding of these phenomena, achieved recently. In contrast to tile first theoretical calculations for conductivity tensor components many inodem authors are trying to take into account a quasi one-dimensional character of electron dynamic, that leads to the Anderson localization (AL) of electrons in the random potential of chaotically distributed charged impurities in ultra-quantum limit (UQL). In 1978 Abrikosov and Ryzlddn tried to summarize diagrams of higher order in the perturbation theory, but they succeeded only in the case of short range impurity potential, that really did not lead to AL [1]. Therefore their result practically coincide with previous received from kinetic equation. For the most interesting case of charged impurities, that have a long range Coulomb potential, they had to use only a scaling hypothesis. Murzin [2] and Poliakov [3] following Dreizin and Dykhne [4] had taken into account tile correlation in scattering acts on charged impurities because of and probability of an electron returns to the same crystal regions. Later Murzin combined this idea with conception of AL. In his model AL could be destroyed by a transverse displacement of these localized states because of electric drifting in magnetic and electric fields crossed to each other [5]. Within the framework of the oneelectron model in the case of a classical screening (CS) he received the following behaviors of dependencies for longitudinal and transverse components of conductivity tensor: o,, QcH -6 and o~, ocH s~. In our previous paper [6] we had taken into account, that the opposite case of quantum screening (QS) occupied a significant part of the UQL region. For QS case, where a wave length of Fermi electrons XF became more, than a radius of screening r,. our calculations gave quite different dependencies: r ocH 2 and oxx ocH ~ Their comparison with the experimental data for n-htSb had shown that for a such material it was impossible to observe CS and QS regions separatly, because an extent of the UQL region was limited by magnetic freeze out effect, that is really a ease of metal-dielectric or the Mort transition (MT).