Kondo effect in Fermi systems with a gap: A renormalization-group study

We present the results of a Wilson renormalization-group study of the single-impurity Kondo and Anderson models in a system with a gap in the conduction-electron spectrum. The behavior of the impurity susceptibility and the zero-frequency response function, $T〈〈S_z{;S}_z〉〉$ are discussed in the cases with and without particle-hole symmetry. For the case of no particle-hole symmetry, we find a transition, as the bandgap $\Delta$ increases, from a singlet ground state (when $\Delta \ll T_K,$ where $T_K$ is the Kondo temperature) to a doublet ground state (when $\Delta \gg T_K)$. But there is no such transition for the case with particle-hole symmetry: the ground state is always a doublet. In addition, for the asymmetric Anderson model the correlation functions, $〈\overrightarrow{S}\cdot \overrightarrow{\sigma }\mathrm{}\left(0\right)\mathrm{}〉$, $〈n_d〉$, and $〈n_d\left(2\mathrm{}-n_d\right)〉$ are computed.