Kondo screening and random-singlet formation in highly disordered systems

TL;DR

This paper introduces a minimal model to explain the complex low-temperature thermodynamics of doped semiconductors near the metal-insulator transition, emphasizing the competition between Kondo screening and random-singlet formation.

Contribution

It develops a variational approach capturing both Fermi-liquid and random-singlet phases in disordered systems, revealing the evolution of magnetic susceptibility behavior with doping.

Findings

Susceptibility follows a power-law with doping-dependent exponent.

The model reproduces the transition from Fermi-liquid to random-singlet phase.

Highlights the interplay between Kondo effect and disorder in low-temperature physics.

Abstract

We propose a minimal model to capture the anomalous low-temperature thermodynamics of doped semiconductors, such as Si:P, across the metal-insulator transition. We consider pairs of local magnetic moments coupled to a highly disordered, non-interacting electronic bath that undergoes a metal-insulator transition with increasing doping. Using a large-$\mathcal{N}$ variational approach, we capture both the inhomogeneous local Fermi-liquid and the insulating random-singlet phase, and find that the local moment susceptibility exhibits a robust power-law behavior, $\chi(T) \propto T^{-\alpha}$, with $\alpha$ evolving smoothly with doping before saturating in the metal. Our results highlight the competition between Kondo screening and random-singlet formation as the key ingredient in constructing a complete theory for the low-temperature behavior of strongly disordered interacting systems.