Glassy properties of Anderson localization: pinning, avalanches and chaos

TL;DR

This paper uses numerical simulations to explore the glassy phenomena in Anderson localization in two dimensions, revealing pinning, avalanches, and chaos, and connecting these to directed polymer and spin-glass behaviors.

Contribution

It uncovers the glassy properties of Anderson localization, including pinning, avalanches, and chaos, and relates the roughness exponent to directed polymer models.

Findings

Pinning and abrupt changes in quantum transport due to disorder.

Roughness exponent ζ=2/3 matches directed polymer behavior.

Chaos linked to interference effects and conductance fluctuations.

Abstract

I present the results of extensive numerical simulations which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches and chaos. I first show that strong localization confines quantum transport along paths which are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent $\zeta$ characterizing the transverse fluctuations of these paths and find that its value $\zeta=2/3$ is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely the fragility of the conductance with respect to small perturbations in the disorder configuration. It is linked to interference effects and universal conductance fluctuations at weak disorder, and more spin-glass-like behavior at strong disorder.