Anderson-Mott transition as a quantum glass problem

TL;DR

This paper proposes that electrons near the Anderson-Mott transition exhibit glass-like behavior, developing a quantum glass scaling theory that explains experimental anomalies and predicts activated dynamical scaling.

Contribution

It introduces a novel quantum glass scaling framework for the Anderson-Mott transition, linking disordered electron behavior to glassy dynamics and critical phenomena.

Findings

Electrons near the transition show non-self-averaging behavior.

Dynamical scaling follows a generalized Vogel-Fulcher law.

Proposes new experiments to test quantum glass predictions.

Abstract

We combine a recent mapping of the Anderson-Mott metal-insulator transition on a random-field problem with scaling concepts for random-field magnets to argue that disordered electrons near an Anderson-Mott transition show glass-like behavior. We first discuss attempts to interpret experimental results in terms of a conventional scaling picture, and argue that some of the difficulties encountered point towards a glassy nature of the electrons. We then develop a general scaling theory for a quantum glass, and discuss critical properties of both thermodynamic and transport variables in terms of it. Our most important conclusions are that for a correct interpretation of experiments one must distinguish between self-averaging and non-self averaging observables, and that dynamical or temperature scaling is not of power-law type but rather activated, i.e. given by a generalized Vogel-Fulcher law. Recent mutually contradicting experimental results on Si:P are discussed in the light of this, and new experiments are proposed to test the predictions of our quantum glass scaling theory.