The Specific Heat of Na$_{0.3}$CoO$_{2}\cdot$1.3H$_{2}$O: Two Superconducting Gaps

The specific heats (C) of three polycrystalline samples of Na$_{0.3}$CoO$_{2}\cdot $1.3H$_{2}$O were measured in magnetic fields 0 $\le $ B $\le $ 9 T. The first sample was not superconducting, but showed a small antiferromagnetic anomaly at T$_{N}\sim $6 K. Samples two and three showed clean, but broadened, superconducting transitions with T$_{c}$'s of 4.52 and 4.65 K, respectively, and no evidence of magnetic impurities. They have large non-superconducting fractions, and qualitatively different specific heats. In the normal state for both samples $\gamma $ = 16 mJ K$^{-2}$ mol$^{-1}$. For B = 0, both superconducting samples can be fit with two energy gaps (different in magnitude and fraction for each sample), one larger and one smaller than the BCS value. In a plot of C/$\gamma $T vs. T/T$_{c}$ for B = 0 the specific heat of the second sample is strikingly similar to that of MgB$_{2}$, an established two-gap superconductor. The evolution of $\gamma $(B)/$\gamma $ with B in the mixed state for the second sample will be contrasted to that of MgB$_{2}$.