Superconductivity in Na${}_x$CoO${}_2$$\cdot$yH${}_2$O : Is Spin-Charge Separation Protecting a d${}_1$+id${}_2$ State ?

Superconductivity in Na${}_x$CoO${}_2$$\cdot$yH${}_2$O is likely to be a p or d-wave; however, experiments are unable to pinpoint the symmetry. A simple estimate of pair breaking effects from an unavoidable Na$^+$ vacancy disorder' in an ordered Na$^+$ lattice, at an optimal $x_{\rm opt} \approx 0.30$ is shown to destroy a Fermi liquid based p or d-wave superconductivity. However, a robustness of superconducting and normal states, seen in experiments is pointed out and argued to imply presence of a quantum protectorate’, possibly a `spin-charge decoupling’ that protects a d${}_1$+id${}_2$ and not a p-state. A calculation of Knight shift and $\frac{1}{T_1}$ in the framework of RVB mean field theory and a fit to the data of Kobayashi $etal.$ [9] is made.