Specific heat ofNa0.3CoO2⋅1.3H2O: Two energy gaps, nonmagnetic pair breaking, strong fluctuations in the superconducting state, and effects of sample age

The specific heat of three samples of ${\text{Na}}_{0.3}{\text{CoO}}_{2}\ensuremath{\cdot}1.3{\text{H}}_{2}\text{O}$ shows an evolution of the superconductivity and its eventual disappearance with increasing sample age. The specific heat of two superconducting samples is characteristic of a superconductor with two energy gaps, which implies contributions of two electron bands to the Fermi surface. The changes in the specific heat are associated with a nonmagnetic pair-breaking action that progresses with sample age and acts preferentially in the band with the smaller gap to produce an increasing ``residual'' electron density of states and a shift in the relative contributions of the bands to the superconducting condensate. For the nonsuperconducting sample the pair breaking has weakened the superconducting-state electron pairing to the point that it has given way to a competing order. The similarity of the time scale for these changes to that recently reported for the formation of O vacancies suggests a relation between the two effects and the identification of the O vacancies as the pair-breaking scattering centers. Together, these effects provide an understanding of the strong sample dependence of the properties of this material. They also suggest an unusual competition between two effects of the O vacancies: enhancement of the superconductivity at low concentrations by adjusting the carrier concentration and destruction of the superconductivity at high concentrations by pair breaking. Comparison of the coefficient of the normal-state conduction-electron specific heat, ${\ensuremath{\gamma}}_{n}=16.1\text{ }\text{mJ}\text{ }{\text{K}}^{\ensuremath{-}2}\text{ }{\text{mol}}^{\ensuremath{-}1}$, with band-structure calculations supports the existence of the controversial ${e}_{g}^{\ensuremath{'}}$ hole pockets in the Fermi surface, in addition to the well established ${a}_{1g}$ surface. The onset of the transition to the vortex state is independent of magnetic field, suggesting the presence of unusually strong fluctuation effects. The specific-heat results and their implications for band structure and symmetry of the superconducting-state order parameter are compared with other experimental and theoretical results.