Anderson localization: 2-D system in an external magnetic field

TL;DR

This paper extends an analytical approach to study Anderson localization in a 2-D system under a strong magnetic field, revealing critical points with divergent localization lengths that are difficult to detect numerically.

Contribution

It generalizes previous analytical methods to include strong magnetic fields and identifies critical points in each subband associated with Anderson localization.

Findings

Each subband has a critical point with divergent localization length.

Critical points are part of a phase coexistence area.

Numerical methods may miss these critical points due to finite-size limitations.

Abstract

The analytical approach developed by us for the calculation of the phase diagram for the Anderson localization via disorder [J.Phys.: Condens. Matter 14, 13777 (2002)] is generalized here to the case of a strong magnetic field when $q$ subbands ($q=1,2,3$) arise. It is shown that in a line with the generally accepted point of view, each subband is characterized by a critical point with a divergent localization length $\xi$ which reveals anomaly in energy and disorder parameters. These critical points belong to the phase coexistence area which cannot be interpreted by means of numerical investigations. The reason for this is a logical incompleteness of the algorithm used for analysis of a computer modelling for finite systems in the parameter range where the finite-size scaling is no longer valid.