Magnetic impurities in gapless Fermi systems: perturbation theory

Journal article

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, ΔI ∝ |ω|r 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 A(ω) = |ω|r D(ω) is pinned at the Fermi level ω = 0 for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon D(ω = 0) 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 r < 1/2 and r > 1 but not for 1/2 < r < 1. 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.

Authors: Glossop, M; Logan, D

• Publication status: Published
• Journal: EUROPEAN PHYSICAL JOURNAL B
• Volume: 13
• Issue: 3
• Pages: 513-525
• Publication date: 2000-02-01
• DOI: 10.1007/s100510050063
• ISSN: 1434-6028
• Language: English
• Keywords: 72.15.Qm Scattering mechanisms and Kondo effect; 75.20.Hr Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions