Magnetic Impurity in Insulators with Small Energy Gap

Abstract

Static and dynamic properties of a magnetic impurity in insulators with a small energy gap are investigated by the poor man's scaling, 1/ N expansion, the self-consistent perturbation method within the non-crossing approximation (NCA) and the quantum Monte Carlo (QMC) method. It is shown that the ground state of the magnetic impurity changes from the singlet to multiplet when the gap increases, as in the case of the magnetic impurity in a BCS superconductor, although there is a different feature compared to the latter. Critical value of the gap E c is found to be E c / T K =2.0 by 1/ N expansion and NCA, while E c / T K ≈0.4∼0.9 by QMC, where T K denotes the Kondo temperature. It is found by the poor man's scaling that E c is enhanced (reduced) by the enhanced (rounded) gap-edge.