Orbital physics in the sodium cobalt oxyhydrate superconductor NA_xCoO₂ · yH₂O

The orbital physics of superconductors with strongly correlated electrons remains to be one of the unexplored fields of the condensed-matter physics. This is mainly because there has been no established example of the multiorbital superconductor. In this article, we argue that in the recently discovered sodium cobalt oxyhydrate NA_xCoO₂ · yH₂O, the Co t_2g orbitals play essential roles on the mechanism and properties of its superconductivity, and this material, thus, provides a precious example of the long-desired multiorbital superconductor. We review recent developments of theoretical studies, which focus on the orbital degrees of freedom, and also related experimental studies. We particularly focus on experimentally obtained phase diagrams, which reveal that superconducting and magnetic properties of the present cobaltate are sensitively controlled by the CoO₂-layer thickness owing to the orbital-lattice coupling. By constructing and analyzing multiorbital models, we study effects of the CoO₆ lattice distortion. We reproduce the phase diagrams, and propose that two different superconducting states, i.e. a spin-singlet extended s-wave pairing and a spin-triplet p-wave pairing, on different types of Fermi surfaces are possibly realized. In particular, the latter p-wave pairing was stabilized by ferromagnetic fluctuations induced by the interorbital Hund’s-rule coupling. By microscopically calculating thermodynamic quantities, we show that controversial and inconsistent results of several thermodynamic measurements can be well understood if we consider these two kinds of superconducting states. Through this discussion, we propose several fascinating properties, pairing mechanisms, and phenomena originating from the orbital-lattice coupling, the Hund’s-rule coupling, the spin-orbit interaction, and the multiband superconducting gap, which are inherent in the multiorbital systems, and can never be expected in usual single-band superconductors like high-Tc cuprates and organics. We point out that this cobaltate system can be a key material for studying the orbital physics in the strongly correlated superconductors.