Weak coupling theory of multicomponent superconductors.

We consider the pairing state due to the BCS mechanism in substances of cubic, hexagonal, or tetragonal symmetry, where the superconducting parameter is multicomponent, i.e., transforms according to either a 2-dimensional or a 3-dimensional representation of the crystal point group. We show that the superconducting phase always breaks the time-reversal symmetry for singlet multicomponent superconductors. For triplet superconductors, the superconducting order parameter turns out to be always non-magnetic in the cubic group, ferromagnetic in tetragonal, and either ferromagnetic ($E_{1u}$ representation) or non-magnetic ($E_{2u}$ representation) in hexagonal group. According to these results, for example, the superconducting phases in both Sr$_2$RuO$_4$ and Na$_x$CoO$_2$-yH$_2$O should be ferromagnetic.