Upper critical field in the superconducting Kondo lattice

The upper critical field $H_{c2}$ in the Kondo lattice was theoretically studied in connection with superconductivity in ${\mathrm{CeCu}}_2$ ${\mathrm{Si}}_2$ and ${\mathrm{UBe}}_{13}$. To describe the coherent state in the Kondo lattice, a periodic Anderson model with multiple conduction bands was used. With the use of a single-site approximation for the self-energy of the f electron, a Fermi-liquid state was derived in the presence of external magnetic field. By assuming a singlet superconductivity of the Fermi liquid, $H_{c2}$ was calculated as a function of temperature and the scattering potentials due to impurities. In comparison with the experiments in ${\mathrm{CeCu}}_2$ ${\mathrm{Si}}_2$ and ${\mathrm{UBe}}_{13}$, the nature of superconductivity in these compounds—that is, singlet or triplet superconductivity—was discussed.