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Register a new userHeat Capacity of Na$_{0.3}$CoO$_{2}$$cdot$1.3H$_{2}$O, a New Two-Gap Superconductor: Comparison with the Heat Capacity of MgB$_2$
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The superconducting-state heat capacity of Na$_{0.3}$CoO$_{2}$$cdot$1.3H$_{2}$O shows unusual, marked deviations from BCS theory, at all temperatures. At low temperatures the heat capacity has the $T^2$ dependence characteristic of line nodes in the energy gap, rather than the exponential temperature dependence of a fully gapped, conventional superconductor. At temperatures of the order of one fifth of the critical temperature and above, the deviations are strikingly similar to those of MgB$_2$, which are known to be a consequence of the existence of substantially different energy gaps on different sheets of the Fermi surface. A two-gap fit to the Na$_{0.3}$CoO$_{2}$$cdot$1.3H${_2}$O data gives gap amplitudes of 45% and 125% of the BCS value, on parts of the Fermi surface that contribute, respectively, 45% and 55% to the normal-state density of states. The temperature of the onset of the transition to the vortex state is independent of magnetic field, which shows the presence of unusually strong fluctuations.
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In order to investigate the role of the water molecules in Na$_{0.35}$CoO$_{2}cdot$1.3H$_{2}$O, we synthesized superconducting Na$_{0.35}$CoO$_{2}cdot$1.3H$_{2}$O and nonsuperconducting Na$_{0.35}$CoO$_{2}cdot$0.7H$_{2}$O, and measured their normal-state magnetic susceptibilities. The susceptibility of Na$_{0.35}$CoO$_{2}cdot$1.3H$_{2}$O has an enhancement below ~150 K probably caused by ferromagnetic fluctuation, whereas no such enhancement was observed in Na$_{0.35}$CoO$_{2}cdot$0.7H$_{2}$O. The water molecules in Na$_{0.35}$CoO$_{2}cdot$1.3H$_{2}$O may work to shield random coulomb potential of the Na ions with smoother potential at the CoO$_{2}$ layer. This effect may account for the appearance of superconductivity in Na$_{0.35}$CoO$_{2}cdot$1.3H$_{2}$O.
The cobaltates have demonstrated a wide variety complex behavior. The Na rich region of the phase diagram displays various degrees of anomalous behavior, such as Curie-Weiss behavior near a band insulatorcite{Foo:2004}, charge disproportionationcite{Mukhamedshin:2005}, and non-Fermi-liquid behavior in the resistivitycite{Foo:2004}. Alternatively, the Na poor region of the phase diagram appears to be a Fermi-liquid. The magnetic susceptibility displays Pauli behavior, the resistivity is roughly quadratic at low temperaturescite{Foo:2004}, and the system appears to be homogeneouscite{Mukhamedshin:2005}. Therefore, the Na poor region of the phase diagram seems like a natural starting point to attempt to explain the ARPES experiments and heat capacity measurements from a quantitative standpoint.
The single electron tunneling spectroscopy on superconductor Na$_{x}$CoO$_2$$cdot$ yH$_2$O and its starting compound Na$_{x}$CoO$_2$ has been studied with point-contact method. The spectra of Na$_{x}$CoO$_2$ have two types of distinct shapes at different random locations, this is attributed to the non-uniformly distributed sodium escaped from the inner part of the sample. While all the measured spectra of the superconducting samples Na$_{x}$CoO$_2$$cdot$ yH$_2$O have a good spatial reproducibility, and show a remarkable zero bias conductance depression appearing below an onset temperature which associates very well with the resistance upturn at around 45 K. The latter behavior resembles in some way the pseudogap feature in high-T$_c$ cuprate uperconductors.
High-energy (h$ u$ = 5.95 keV) synchrotron Photoemission spectroscopy (PES) is used to study bulk electronic structure of Na$_{0.35}$CoO$_{2}$.1.3H$_{2}$O, the layered superconductor. In contrast to 3-dimensional doped Co oxides, Co $it{2p}$ core level spectra show well-separated Co$^{3+}$ and Co$^{4+}$ ions. Cluster calculations suggest low spin Co$^{3+}$ and Co$^{4+}$ character, and a moderate on-site Coulomb correlation energy U$_{dd}sim$3-5.5 eV. Photon dependent valence band PES identifies Co $it{3d}$ and O $it{2p}$ derived states, in near agreement with band structure calculations.
A weak magnetic order was found in a non-superconducting bilayered-hydrate Na$_{x}$CoO$_{2}cdot y$H$_{2}$O sample by a Co Nuclear Quadrupole Resonance (NQR) measurement. The nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ shows a prominent peak at 5.5 K, below which a Co-NQR peak splits due to an internal field at the Co site. From analyses of the Co NQR spectrum at 1.5 K, the internal field is evaluated to be $sim$ 300 Oe and is in the $ab$-plane. The magnitude of the internal field suggests that the ordered moment is as small as $sim 0.015$ $mu_B$ using the hyperfine coupling constant reported previously. It is shown that the NQR frequency $ u_Q$ correlates with magnetic fluctuations from measurements of NQR spectra and $1/T_1T$ in various samples. The higher-$ u_Q$ sample has the stronger magnetic fluctuations. A possible phase diagram in Na$_{x}$CoO$_{2}cdot y$H$_{2}$O is depicted using $T_c$ and $ u_Q$, in which the crystal distortion along the c-axis of the tilted CoO$_2$ octahedron is considered to be a physical parameter. Superconductivity with the highest $T_c$ is seemingly observed in the vicinity of the magnetic phase, suggesting strongly that the magnetic fluctuations play an important role for the occurrence of the superconductivity.
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