A Local Moment Approach to magnetic impurities in gapless Fermi systems

TL;DR

This paper develops a comprehensive local moment approach for the Anderson impurity model with a soft-gap hybridization, capturing key regimes and phase transitions, and aligns well with numerical renormalization group results.

Contribution

It introduces a unified theory for single-particle excitations in a soft-gap AIM, covering all energy scales and phases, with asymptotically exact results and new predictions.

Findings

Agreement with NRG studies on spectra and phase boundaries

Universal scaling form for spectra near phase boundary for r<1/2

Recovery of Fermi liquid behaviour as r approaches 0

Abstract

A local moment approach is developed for the single-particle excitations of a symmetric Anderson impurity model (AIM), with a soft-gap hybridization vanishing at the Fermi level with a power law r > 0. Local moments are introduced explicitly from the outset, and a two-self-energy description is employed in which the single-particle excitations are coupled dynamically to low-energy transverse spin fluctuations. The resultant theory is applicable on all energy scales, and captures both the spin-fluctuation regime of strong coupling (large-U), as well as the weak coupling regime. While the primary emphasis is on single particle dynamics, the quantum phase transition between strong coupling (SC) and (LM) phases can also be addressed directly; for the spin-fluctuation regime in particular a number of asymptotically exact results are thereby obtained. Results for both single-particle spectra and SC/LM phase boundaries are found to agree well with recent numerical renormalization group (NRG) studies. A number of further testable predictions are made; in particular, for r < 1/2, spectra characteristic of the SC state are predicted to exhibit an r-dependent universal scaling form as the SC/LM phase boundary is approached and the Kondo scale vanishes. Results for the `normal' r = 0 AIM are moreover recovered smoothly from the limit r -> 0, where the resultant description of single-particle dynamics includes recovery of Doniach-Sunjic tails in the Kondo resonance, as well as characteristic low-energy Fermi liquid behaviour.