Effect of Anisotropy on the Localization in a Bifractal System

TL;DR

This study investigates how anisotropy affects electron localization in a bifractal system, finding that anisotropy does not influence the critical properties of localization in this structure.

Contribution

The paper provides numerical analysis of localization lengths in a bifractal system, demonstrating that anisotropy does not alter critical localization properties.

Findings

Localization lengths are calculated along the fractal structure.

Critical disorder and exponents are obtained from finite size scaling.

Anisotropy is shown to be irrelevant to localization criticality.

Abstract

Bifractal is a highly anisotropic structure where planar fractals are stacked to form a 3-dimensional lattice. The localization lengths along fractal structure for the Anderson model defined on a bifractal are calculated. The critical disorder and the critical exponent of the localization lengths are obtained from the finite size scaling behavior. The numerical results are in a good agreement with previous results which have been obtained from the localization lengths along the perpendicular direction. This suggests that the anisotropy of the embedding lattice structure is irrelevant to the critical properties of the localization.