Behavior of magnetic impurities in gapless Fermi systems

In a number of systems, including certain semiconductors and unconventional superconductors, the effective density of states varies near the Fermi energy like $|E-E_F|^r$. The behavior of dilute magnetic impurities in such systems is studied using a non-perturbative renormalization-group approach. Close to particle-hole symmetry, the Kondo effect is suppressed for the cases of greatest relevance ($r=1$ and $2$). Away from this symmetry, any quenching of the impurity moment is accompanied by a low-temperature decrease in the impurity resistivity, rather than the increase found in metals.