A Kondo impurity in a disordered metal: Anderson's theorem revisited

TL;DR

This paper proves an Anderson-like theorem for a Kondo impurity in a weakly disordered metal, showing that low-temperature thermodynamics are unaffected by disorder strength and realization in the large-N limit.

Contribution

It establishes a novel Anderson theorem for a disordered Kondo system, demonstrating disorder independence of thermodynamics and fluctuations in the large-N approximation.

Findings

Disorder-averaged thermodynamics are independent of disorder strength at low temperatures.

Fluctuation effects are unaffected by specific disorder realizations.

The theorem connects to experimental and theoretical studies of disordered Kondo systems.

Abstract

We consider a local moment which is coupled by a non-random Kondo $J$ to a band of conduction electrons in a random potential. We prove an analog of Anderson's theorem in a large-N limit of this model. The theorem states that when the disorder is weak, the disorder-averaged low-temperature thermodynamics is independent of the strength of the disorder; remarkably, it further states that fluctuation effects in the long-time limit are {\it independent even of the realization of the disorder}. We discuss the relationship of this theorem to theoretical and experimental studies of similar problems.