A local moment approach to magnetic impurities in gapless Fermi systems

A local moment approach is developed for single-particle excitations of a symmetric Anderson impurity model (AIM) with a soft-gap hybridization vanishing at the Fermi level: icons/Journals/Common/Delta" ALT="Delta" ALIGN="TOP"/> _I icons/Journals/Common/propto" ALT="propto" ALIGN="TOP"/> |icons/Journals/Common/omega" ALT="omega" ALIGN="TOP"/> |^r , with r >0. Local moments are introduced explicitly from the outset, and a two-self-energy description is employed in which 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 where it is perturbatively exact for those r -domains in which perturbation theory in U is non-singular. While the primary emphasis is on single-particle dynamics, the quantum phase transition between strong-coupling (SC) and local moment (LM) phases can also be addressed directly; for the spin-fluctuation regime in particular a number of asymptotically exact results are thereby obtained, notably for the behaviour of the critical U _c (r ) separating SC/LM states and the Kondo scale icons/Journals/Common/omega" ALT="omega" ALIGN="TOP"/> _m (r ) characteristic of the SC phase. Results for both single-particle spectra and SC/LM phase boundaries are found to agree well with recent numerical renormalization group (NRG) studies; and a number of further testable predictions are made. Single-particle spectra are examined systematically for both SC and LM states; in particular, for all 0icons/Journals/Common/leq" ALT="leq" ALIGN="TOP"/> 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 ricons/Journals/Common/rightarrow" ALT="rightarrow" ALIGN="TOP"/> 0, where the resultant description of single-particle dynamics includes recovery of Doniach-Sunjic tails in the wings of the Kondo resonance, as well as characteristic low-energy Fermi liquid behaviour and the exponential diminution with U of the Kondo scale itself. The normal AIM is found to represent a particular case of more generic behaviour characteristic of the r >0 SC phase which, in agreement with conclusions drawn from recent NRG work, may be viewed as a non-trivial but natural generalization of Fermi liquid physics.