Theoretical studies of unconventional superconductivity in cubic superconductors

In this thesis we study unconventional superconductivity in superconductors having a cubic point group symmetry. We first look at the possibility of a competing superconducting order in cubic A15 superconductors. Competing pairing channels have been proposed in superfluid 3He, in the high temperature cuprate superconductors, and pnictide superconductors. While strong experimental support exists for this in superfluid 3He, the case for superconductors is weaker. In this work we present microscopic arguments to show that A15 superconductors have a competing d-wave order in addition to usual s-wave superconductivity. We also give arguments that provide a unifying explanation for a series of diverse experimental results on the A15 superconductors.;We then use a weak-coupling theory for unconventional superconductors with cubic or tetrahedral point group symmetry to identify all stable superconducting states in zero applied field. We further examine the possibility of having multiple superconducting transitions using weak coupling theories. In hexagonal UPt3, these theories easily give rise to multiple transitions. However, we find that for cubic materials with multiple superconducting transitions, there is only one case in which two superconducting transitions occur within a weak coupling theory. This sequence of transitions however does not agree with the observed properties of a cubic heavy Fermion superconductor PrOs 4Sb12. We provide an example of a theory that agrees with the observed properties of PrOs4Sb12.