Superconductivity in the Kondo lattice

Abstract

Superconductivity in the Kondo lattice was theoretically studied in connection with superconductivity in Ce${\mathrm{Cu}}_2$ ${\mathrm{Si}}_2$ and U${\mathrm{Be}}_{13}$. To achieve superconductivity in these systems, coherence between Ce ions or U ions is of crucial importance. To take account of the coherence, the periodic Anderson model with a small dispersion of the $f$ band was used. With the use of a single-site approximation for the self-energy of the $f$ electron, the heavy fermion state near the Fermi level was derived. This state is a highly correlated state, and the Coulomb repulsive interaction is strongly reduced. The $f$ electrons are found to be responsible for superconductivity. Both the specific heat in the normal state $C_N\mathrm{}\left(T\right)\mathrm{}$ and the specific-heat jump $\Delta C$ at $T_c$ are very large, and the ratio $\frac{\Delta C}{C_N\left(T_c\right)}$ has the BCS value in the weak-coupling approximation. The thermodynamic critical field is very high.