| We present a systematic exposition of the theory of unconventional superconductivity applied to the heavy-fermion superconductor PrOs4Sb12. We begin with a review of conventional and unconventional BCS weak-coupling theory and phenomenology, We then move to a description of this BCS theory applied to three phenomena: the clean-limit thermodynamics, the effect of impurity scattering upon the thermodynamics, and the upper critical magnetic field. All analyses are conducted for both the A phase and B phase of this material.;For the clean-limit thermodynamics, we study the quasiparticle density-of-states, the temperature-dependent order parameter, and the temperature dependence of the specific heat, superfluid density, and critical magnetic field. For the impurity scattering thermodynamics, we consider the effect of strong impurity scattering in the unitary limit and calculate the same quantities calculated for the clean-limit thermodynamics, with the addition of the nuclear spin lattice relaxation rate T1-1. All calculations are performed for three different levels of impurity scattering.;Finally, we consider the upper critical magnetic field Hc2 in both phases of this material. We calculate the temperature dependence of this field and extract the Fermi velocity from these calculations. |
