On Magnetic Impurities in Gapless Fermi Systems

TL;DR

This paper investigates how magnetic impurities behave in gapless Fermi systems with a power-law density of states, revealing a transition from screened to unscreened impurity spins depending on coupling strength.

Contribution

It models the impurity behavior in systems with a power-law density of states using the non-crossing approximation, identifying a transition between Kondo screening and magnetic ground states.

Findings

Transition from Kondo singlet to magnetic ground state identified.

Impurity magnetic susceptibility behavior distinguishes phases.

Complete screening occurs at strong coupling.

Abstract

In ordinary metals, antiferromagnetic exchange between conduction electrons and a magnetic impurity leads to screening of the impurity spin below the Kondo temperature, $T_K$. In systems such as semimetals, small-gap semiconductors and unconventional superconductors, a reduction in available conduction states near the chemical potential can greatly depress $T_K$. The behavior of an Anderson impurity in a model with a power-law density of states, $N(\epsilon) \sim |\epsilon|^r$, $r>0$, for $|\epsilon| < \Delta$, where $\Delta \ll D$, is studied using the non-crossing approximation. The transition from the Kondo singlet to the magnetic ground state can be seen in the behavior of the impurity magnetic susceptibility $\chi$. The product $T\chi$ saturates at a finite value at low temperature for coupling smaller than the critical one. For sufficiently large coupling $T\chi \to 0$, as $T \to 0$, indicating complete screening of the impurity spin.