Kondo screening in gapless magnetic alloys

TL;DR

This paper investigates how a gapless host environment affects Kondo impurity behavior, revealing a transition from Kondo to Anderson regimes driven by a parameter related to the host's density of states, using Bethe ansatz analysis.

Contribution

It provides a detailed analysis of Kondo screening in gapless magnetic alloys, identifying the conditions for regime transitions and the effects of potential scattering, which were not previously understood.

Findings

Transition from Kondo to Anderson regime driven by parameter _r.

Weak magnetic fields cause impurity spin to exceed free value in the Anderson regime.

Strong potential scattering destroys the Anderson regime.

Abstract

The low-energy physics of a spin-1/2 Kondo impurity in a gapless host, where a density of band states $\rho_0(\epsilon)=|\epsilon|^r/(|\epsilon|^r+\beta^r)$ vanishes at the Fermi level $\epsilon=0$, is studied by the Bethe ansatz. The growth of the parameter $\Gamma_r=\beta{\rm g}^{-1/r}$ (where ${\rm g}$ is an exchange constant) is shown to drive the system ground state from the Kondo regime with the screened impurity spin to the Anderson regime, where the impurity spin is unscreened, however, in a weak magnetic field $H$, it exceeds its free value, $S_i(H)>{1/2}$, due to a strong coupling to a band. It is shown also that a sufficiently strong potential scattering at the impurity site destroys the Anderson regime.