Magnetic impurities in gapless Fermi systems: perturbation theory |
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Authors: | MT Glossop DE Logan |
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Institution: | (1) Oxford University, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX13QZ, UK, GB |
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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>0case: 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.
Received 26 August 1999 |
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Keywords: | PACS 72 15 Qm Scattering mechanisms and Kondo effect - 75 20 Hr Local moment in compounds and alloys Kondo effect valence fluctuations heavy fermions |
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