Magnetic impurities in gapless Fermi systems: perturbation theory
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چکیده
We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, ∆I ∝ |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|rD(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. Magnetic impurities in gapless Fermi systems: perturbation theory 2
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تاریخ انتشار 1999