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, $N(\epsilon) \sim |\epsilon|^r$, $r>0$, for $|\epsilon| < \Delta$, where $\Delta \ll D$, 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 $T\chi \to 0$, as $T \to 0$, indicating complete screening of the impurity spin.