The Kondo Effect in a System with a Singular Density of States

In a number of fermion systems, the quasiparticle density of states varies near the Fermi energy like |E−EF |r, where r = 1 or 2. The effect of magnetic impurities in such systems is studied via a perturbative renormalization-group treatment of the n-channel Kondo model, carried out to third order in the antiferromagnetic exchange coupling J . For 0 < r < 1/2n, a (multichannel) Kondo effect occurs only if J exceeds a critical value Jc(r); otherwise the impurity moment decouples from the Fermi sea at low temperatures. For r > 1/2n, the exchange always renormalizes to zero, whatever the value of J . Strictly, this analysis is valid only in the limits r 1 and n 1. Extension to the conventional Kondo model (n = 1) and larger r is discussed.