Eur. Phys. J. B 13, 513-525 (2000)
https://doi.org/10.1007/s100510050063

Magnetic impurities in gapless Fermi systems: perturbation theory

Oxford University, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX13QZ, UK

Received: 26 August 1999
Published online: 15 February 2000

Abstract

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r> 0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U> 0 case: it exhibits both strong coupling (SC) states (for r< 1) and local moment states (for r> 1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U> 0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r> 1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength.