Universal Distribution of Kondo Temperatures in Dirty Metals

TL;DR

This paper demonstrates that the distribution of Kondo temperatures in disordered metals follows a universal power-law form near zero temperature, with the exponent depending solely on dimensionality, affecting thermodynamic behavior across metal-insulator transitions.

Contribution

It analytically and numerically establishes a universal distribution of Kondo temperatures in disordered systems, highlighting its dependence on dimensionality and implications for phase transitions.

Findings

Distribution P(T_K) follows a universal power-law near zero T_K.

Exponent epends only on the system's dimensionality.

Thermodynamic properties vary smoothly across the metal-insulator transition.

Abstract

Kondo screening of diluted magnetic impurities in a disordered host is studied analytically and numerically in one, two and three dimensions. It is shown that in the T_K \to 0 limit the distribution of Kondo temperatures has a universal form, P(T_K) \sim T_K^{-\alpha} that holds in the insulating phase and persists in the metallic phase close to the metal insulator transition. Moreover, the exponent \alpha depends only on the dimensionality. The most important consequence of this result is that the T-dependence of thermodynamic properties is smooth across the metal-insulator transition in three dimensional systems.