Anisotropic Localization Effect in Layered Materials

TL;DR

This paper explores how anisotropy affects electron localization in layered materials similar to high-Tc cuprates, revealing a crossover from 2D to 3D behavior and discussing implications for resistivity.

Contribution

It identifies a critical anisotropy level where a 2D-3D crossover occurs and analyzes anisotropic localization effects in layered disordered systems.

Findings

A crossover from 2D to 3D localization behavior at a critical interlayer hopping.

Existence of anisotropic localization effects in finite systems.

Anisotropic localization does not explain the c-axis resistivity in high-Tc cuprates.

Abstract

We investigate localization properties in the highly anisotropic and intrinsically disordered layered material, which is analogous to high-Tc cuprates. By varying the anisotropy of the system which is parameterized by the interlayer hopping $tp$, we find a crossover from two-dimensional (2D) to three-dimensional (3D) behavior at a critical hopping amplitude $tp_c$, where a mobility edge starts to appear. We show that below the mobility edge, anisotropic localization effect may exist for a finite size system, when the $ab$-plane localization length is longer than the system size and the $c$-axis localization length is shorter than the system size. Nevertheless, we argue that such anisotropic localization can not account for the ``semiconductor'' like behavior of the $c$-axis resistivity of high $\Tc$ cuprates.