Superconducting states of reduced symmetry: General order parameters and physical implications

It is shown that the order parameter in reduced-symmetry superconductors can be represented in terms of a complete set of basis-function multiplets, which is analogous to a complete set of crystal harmonics. These complete sets are found for several symmetries that are germane to the study of heavy-fermion superconductors. The implications of a general order parameter are discussed for several physical properties: line nodes in the energy gap, the Knight shift, surface pair-breaking, and time-reversal symmetry.