CoO₂-layer-thickness dependence of magnetic properties and possible two different superconducting states in Na_xCoO ₂·yH₂O

In order to understand the experimentally proposed phase diagrams of Na_xCoO₂·yH₂O, we theoretically study the CoO₂-layer-thickness dependence of its magnetic and superconducting (SC) properties by analyzing a multiorbital Hubbard model using the random phase approximation. When the Co valence s is +3.4, we show that the magnetic fluctuation exhibits a strong layer-thickness dependence, where it is enhanced at finite (zero) momentum in the thicker (thinner) layer system. A magnetic order phase appears sandwiched by two SC phases, consistent with the experiments. These two SC phases have different pairing states, where one is the singlet extended s-wave state and the other is the triplet p-wave state. On the other hand, only a triplet p-wave SC phase with a dome-shaped behavior of T_c is predicted when s = +3.5, which is also consistent with the experiments. Controversial experimental results on the magnetic properties are also discussed.