Specific Heat of Na$_{0.35}$CoO$_{2}\cdot $1.3H$_{2}$O: Effects of Sample Age; Two Energy Gaps; Non-Magnetic Pair Breaking

Specific-heat measurements on three samples of Na$_{0.35}$CoO$_{2}\cdot $1.3H$_{2}$O show an evolution of the superconductivity and its eventual disappearance with increasing sample age. The results, in combination with other recent work [1], provide a basis for understanding the extreme ``sample dependence'' of the properties of this material. Samples of different age are in effect samples of slightly different materials: A non-magnetic pair-breaking action produces a residual density of electron states that increases with sample age. It occurs preferentially in the electron band (one of two with different energy gaps) with the smaller gap, producing a change in the nature of the superconducting condensation. It also weakens the overall electron pairing of the superconducting state until it gives way to a competing ordering, possibly a CDW. The same combinations of features in the specific heat have been seen in measurements on other individual samples, showing that they are ``intrinsic''. The changes in the specific heat are evidently related to structural and electronic changes that occur on a similar time scale [1], and include an increasing concentration of O vacancies, which could be the pair-breaking scattering centers. \newline [1] P. W. Barnes et al., Phys. Rev. B \textbf{72}, 134515 (2005).