Localization in Quasi-1D Systems with Random Magnetic Field

Abstract

We investigate the localization of electrons hopping on quasi-1D strips in the presence of random magnetic field. In the weak-disorder region, by perturbative analytical techniques, we derive scaling laws for the localization length, $ξ$, of the form $ ξ\propto \frac{1}{w^η}$, where $w$ is the size of magnetic disorder and the exponent $η$ assumes different values in the various energy ranges. Moreover, in the neighborhood of the energies where a new channel opens a certain rearrangement of the perturbation expansion leads to scaling functions for $ξ$. Although the latter are in general quantitatively wrong, they correctly reproduce the corresponding $η$ exponents and the form of the scaling variables and are therefore useful for understanding the behavior of $ξ$.