Phase transitions in gapless Fermi systems with magnetic impurities

We consider a model of a Kondo-like impurity interacting with a band of fermions for which the density of states is zero or small near the Fermi energy. Renormalization-group arguments and a large-degeneracy technique are used to demonstrate that this model has a nontrivial zero-temperature phase transition at a finite coupling constant, in contrast to the zero-coupling-constant transition of the ordinary Kondo model. Possible experimental realizations of this model include anisotropic superconductors, narrow-gap semiconductors, and systems with flux phases.