On magnetic impurities in gapless Fermi systems

In ordinary metals, antiferromagnetic exchange between conduction electrons and a magnetic impurity leads to screening of the impurity spin below the Kondo temperature, T-K In systems such as semimetals, small-gap semiconductors and unconventional superconductors, a reduction in available conduction states near the chemical potential can greatly depress T-K. The behavior of an Anderson impurity in a model with a power-law density of states, p(epsilon) proportional to \epsilon\(tau), r > 0, for \epsilon\ < Delta, where Delta is small compared to the bandwidth, is studied using the non-crossing approximation. The transition from the Kondo singlet to the magnetic ground state can be seen in the behavior of the impurity magnetic susceptibility chi. The product T chi saturates at a finite value at low temperature for coupling smaller than the critical one. For sufficiently large coupling T chi --> 0, as T --> 0, indicating a complete screening of the impurity spin.