A phenomenology for multiple phases in the heavy fermion skutterudite superconductor PrOs4Sb12

The two superconducting phases recently discovered in skutterudite PrOs4Sb12 are discussed by using the phenomenological Ginzburg-Landau theory in the cubic (tetrahedral) crystal symmetry T_h. Building on experimental imput coming from the recent thermal conductivity measurements, the structure of the gap functions for these two phases are considered for the spin singlet pairing case. One of the phases lying in the high temperature and high field region (the A phase) is a strongly "anisotropic s-wave" state and another phase (the B phase) is "anisotropic s"+ i d-wave state. The B phase breaks cubic crystal symmetry and time reversal symmetry spontaneously. The cubic symmetry breaking in B-phase causes anomalous crystal strain and it could be seen in the anisotropy of thermal expansions and isothermal elastic constants. As a signal of the time reversal symmetry breaking, it is expected that an internal spontaneous magnetization should be observed by the MuSR measurement.