Simple Model for the Superconductivity of Lanthanum and Uranium

Abstract

It is postulated that La and U have a narrow $f$ band above, but very close to, the Fermi surface. An exchange interaction, antiferromagnetic in sign, between electrons in the $f$ band can lead to nonzero occupation of the $f$ levels in a BCS-type wave function. This $f$-band condensation, through a weak coupling of the $f$ band to the conduction band, enhances a BCS condensation of the conduction electrons. There are two energy gaps, for quasiparticle excitations in the two bands. The critical field at zero temperature is calculated, as is the transition temperature. The predicted isotope effect is extremely small. The ratio between the transition temperature and the energy gap at $T=0\mathrm{}$ depends on the numerical values of the parameters; although this ratio is of order unity, it would not be expected to be too near the BCS value of $\frac{1}{1.75}$.