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$\text{}_{K}$. 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$\text{}_{K}$. The behavior of an Anderson impurity in a model with a power-law density of states, ρ(ε) ∝ |ε|$\text{}^{r}$, r>0, for |ε|<Δp, where Δp 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 χ. The product Tχ saturates at a finite value at low temperature for coupling smaller than the critical one. For sufficiently large coupling Tχ → 0, as T → 0, indicating a complete screening of the impurity spin.