Localization in Highly Anisotropic Systems

TL;DR

This paper investigates how anisotropic hopping affects localization in the Anderson model, revealing that the mobility edge is direction-independent while correlation lengths vary, with critical disorder depending on the coupling type.

Contribution

It provides analytical and numerical insights into anisotropic localization, showing how the critical disorder scales with hopping anisotropy in different geometries.

Findings

Mobility edge is independent of propagation direction.

Correlation length differs between extended and localized sides.

Critical disorder scales as t^{1/4} for planes and t^{1/2} for chains.

Abstract

The localization behavior of the Anderson model with anisotropic hopping integral t for weakly coupled planes and weakly coupled chains is investigated both numerically with the transfer matrix method and analytically within the self-consistent theory of localization. It is found that the mobility edge is independent of the propagating direction. However, the correlation (localization) length in the extended (localized) side of the transition can be very different for the two directions. The critical disorder W$_c$ is found to vary from t$^{1 \over 4}$ for weakly coupled planes to t$^{1 \over 2}$ for weakly coupled chains.