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, TK. In systems such as semimetals, small-gap semiconductors and unconventional superconductors, a reduction in available conduction states near the chemical potential can greatly depress Tx. The behavior of an Anderson impurity in a model with a power-law density of states, p(ε) c|c|r , r > 0 , f o r | ε | < Δ , w h e r e Δi s s m a l l c o m p a r e d t o t h e 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