Kondo-Anderson Transitions

TL;DR

This paper investigates how magnetic impurities interact with disordered electronic systems near the Anderson transition, revealing new phase transitions driven by the interplay of Kondo physics and localization effects.

Contribution

It introduces the concept of Kondo-Anderson transitions, analyzing the formation of free magnetic moments and their impact on the phase diagram near the Anderson transition.

Findings

Finite density of free magnetic moments on the insulating side

Shift of the Anderson transition due to spin-flip scattering

Phase diagram with insulator, semimetal, and metal phases

Abstract

Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical Power law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature $T_{K}$ is derived at the AMIT, in the metallic phase and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field $B$ and at finite temperature $T$. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as function of temperature. We find a phase diagram with finite temperature transitions between insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions (KATs).