A model for unconventional superconductivity of Sr 2 RuO 4 is presented to resolve its puzzle. It is shown that the short-range ferromagnetic spin fluctuations give rise to the triplet pairing with p-like symmetry which is breaking the time-reversal symmetry and has a tiny gap due to the salient shape of the Fermi surface characteristic to Sr 2 RuO 4 . The effect of nonmagnetic-impurity scattering in the unitarity limit is shown to fill up easily the tiny gap giving rise to an appreciable residual density of states, which explains consistently the puzzling properties observed so far.

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It is shown on the basis of the lowest order perturbation expansion with respect to critical fluctuations that the critical fluctuations give rise to an enhancement of the potential scattering of non-magnetic impurities. This qualitatively accounts for the enhancement of the resistivity due to impurities which has been observed in variety of systems near the quantum critical point, while the higher order processes happen to give much larger enhancement as seen from the Ward identity arguments. The cases with dynamical critical exponent z=2 and z=3 are discussed explicitly.

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