Localization Length in Anderson Insulator with Kondo Impurities

TL;DR

This paper investigates how magnetic impurities and Kondo correlations influence the localization length in a 2D Anderson insulator, revealing a critical impurity concentration and reentrant localization behavior.

Contribution

It introduces a model linking Kondo correlations with localization length, showing a critical impurity concentration and reentrant localization regimes in 2D Anderson insulators.

Findings

Unitary localization regime is impossible below a critical impurity concentration.

Reentrant dependence of localization length on conductance g.

Giant magnetoresistance due to sensitivity of Kondo correlations to magnetic fields.

Abstract

The localization length, $\xi$, in a 2--dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, $\tau_s^{-1}$. For antiferromagnetic sign of the exchange, %constant, the time $\tau_s$ is {\em itself a function of $\xi$}, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, $n_{\tiny M}$, is smaller than a critical value, $n_c$. For $n_{\tiny M}>n_c$, the dependence of $\xi$ on the dimensionless conductance, $g$, is {\em reentrant}, crossing over to unitary, and back to orthogonal behavior upon increasing $g$. Sensitivity of Kondo correlations to a weak {\em parallel} magnetic field results in a giant parallel magnetoresistance.