Localization in Quasi-1D Systems with Random Magnetic Field

TL;DR

This paper analytically studies electron localization in quasi-1D systems under random magnetic fields, deriving scaling laws for localization length and analyzing behavior near channel opening energies.

Contribution

It introduces perturbative analytical techniques to derive energy-dependent scaling laws for localization length in quasi-1D systems with random magnetic disorder.

Findings

Localization length scales as 1/w^η in weak disorder

Scaling functions near channel opening energies are qualitatively correct

Exponents η vary across different energy ranges

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, ${\xi}$, of the form $ \xi \propto \frac{1}{w^{\eta}}$, where $w$ is the size of magnetic disorder and the exponent $\eta$ 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 $\xi$. Although the latter are in general quantitatively wrong, they correctly reproduce the corresponding $\eta$ exponents and the form of the scaling variables and are therefore useful for understanding the behavior of $\xi$.