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The two superconducting phases recently discovered in skutterudite ${\mathrm{PrOs}}_{4}{\mathrm{Sb}}_{12}$ are discussed by using the phenomenological Ginzburg-Landau theory based on the the cubic (tetrahedral) crystal symmetry ${T}_{h}.$ Building on experimental input 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, whereas the other phase (the $B$ phase) is an ``anisotropic $s+id$-wave'' state. The B phase breaks cubic crystal symmetry and time reversal symmetry spontaneously. The cubic symmetry breaking in the B phase causes anomalous crystal strains which 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 $\ensuremath{\mu}\mathrm{SR}$ measurement.

physical review. b, condensed matter

Phenomenology for multiple phases in the heavy-fermion skutterudite superconductor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">PrOs</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sb</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Phenomenology for multiple phases in the heavy-fermion skutterudite superconductorPrOs4Sb12