CoO2-layer-thickness dependence of magnetic properties and possible two different superconducting states in NaxCoO2 center dot yH(2)O

In order to understand the experimentally proposed phase diagrams of NaxCoO2 center dot yH(2)O, 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.