Electron-Phonon mechanism for Superconductivity in Na0.35_{0.35}CoO2_2: Valence-Band Suhl-Kondo effect Driven by Shear Phonons

To study the possible mechanism of superconductivity in Na$_{0.35}$CoO$_2$, we examine the interaction between all the relevant optical phonons (breathing and shear phonons) and $t_{2g}(a_{1g}+e_g')$-electrons of Co-ions, and study the transition temperature for a s-wave superconductivity. The obtained $T_{\rm c}$ is very low when the $e_g'$-valence-bands are far below the Fermi level. However, $T_{\rm c}$ is strongly enhanced when the top of the $e_g'$-valence-bands is close to the Fermi level (say -50meV), thanks to interband hopping of Cooper pairs caused by shear phonons. This ``valence-band Suhl-Kondo mechanism'' due to shear phonons is significant to understand the superconductivity in Na$_{0.35}$CoO$_2$. By the same mechanism, the kink structure of the band-dispersion observed by ARPES, which indicates the strong mass-enhancement ($m^\ast/m\sim3$) due to optical phonons, is also explained.Comment: 5 pages, 4 figures; v2:Added references, published in J. Phys. Soc. Jp

Spin Dynamics at the Mott Transition and in the Metallic State of the Cs_{3}C_{60} Superconducting Phases

We present here ^{13}C and ^{133}Cs NMR spin lattice relaxation T_{1} data in the A15 and fcc-Cs_{3}C_{60} phases for increasing hydrostatic pressure through the transition at p_{c} from a Mott insulator to a superconductor. We evidence that for p>> p_{c} the (T_{1}T)^{-1} data above T_{c} display metallic like Korringa constant values which match quantitatively previous data taken on other A_{3}C_{60} compounds. However below the pressure for which T_{c} goes through a maximum, (T_{1}T)^{-1} is markedly increased with respect to the Korringa values expected in a simple BCS scenario. This points out the importance of electronic correlations near the Mott transition. For p > p_{c} singular T dependences of (T_{1}T)^{-1} are detected for T >> T_{c}. It will be shown that they can be ascribed to a large variation with temperature of the Mott transition pressure p_{c} towards a liquid-gas like critical point, as found at high T for usual Mott transitions.Comment: 6 pages, 6 figures, submitted to EP

Generalized relation between the relative entropy and dissipation for nonequilibrium systems

Recently, Kawai, Parrondo, and Van den Broeck have related dissipation to time-reversal asymmetry. We generalized the result by considering a protocol where the physical system is driven away from an initial thermal equilibrium state with temperature $\beta_0$ to a final thermal equilibrium state at a different temperature. We illustrate the result using a model with an exact solution, i.e., a particle in a moving one-dimensional harmonic well.Comment: 4 page

Incidence of the Tomonaga-Luttinger liquid state on the NMR spin lattice relaxation in Carbon Nanotubes

We report 13C nuclear magnetic resonance measurements on single wall carbon nanotube (SWCNT) bundles. The temperature dependence of the nuclear spin-lattice relaxation rate, 1/T1, exhibits a power-law variation, as expected for a Tomonage-Luttinger liquid (TLL). The observed exponent is smaller than that expected for the two band TLL model. A departure from the power law is observed only at low T, where thermal and electronic Zeeman energy merge. Extrapolation to zero magnetic field indicates gapless spin excitations. The wide T range on which power-law behavior is observed suggests that SWCNT is so far the best realization of a one-dimensional quantum metal.Comment: 5 pages, 4 figure

59Co Nuclear Quadrupole Resonance Studies of Superconducting and Non-superconducting Bilayer Water Intercalated Sodium Cobalt Oxides NaxCoO2.yH2O

We report 59Co nuclear quadrupole resonance (NQR) studies of bilayer water intercalated sodium cobalt oxides NaxCoO2.yH2O (BLH) with the superconducting transition temperatures, 2 K < T_c <= 4.6 K, as well as a magnetic BLH sample without superconductivity. We obtained a magnetic phase diagram of T_c and the magnetic ordering temperature T_M against the peak frequency nu_3 59Co NQR transition I_z = +- 5/2 +-7/2 and found a dome shape superconducting phase. The 59Co NQR spectrum of the non-superconducting BLH shows a broadening below T_M without the critical divergence of 1/T_1 and 1/T_2, suggesting an unconventional magnetic ordering. The degree of the enhancement of 1/T_1T at low temperatures increases with the increase of nu_3 though the optimal nu_3~12.30 MHz. In the NaxCoO2.yH2O system, the optimal-T_c superconductivity emerges close to the magnetic instability. T_c is suppressed near the phase boundary at nu_3~12.50 MHz, which is not a conventional magnetic quantum critical point.Comment: 4 pages, 5 figure

CoO2-Layer-Thickness Dependence of Magnetic Properties and Possible Two Different Superconducting States in NaxCoO2.yH2O

In order to understand the experimentally proposed phase diagrams of NaxCoO2.yH2O, we theoretically study the CoO2-layer-thickness dependence of magnetic and superconducting (SC) properties by analyzing a multiorbital Hubbard model using the random phase approximation. When the Co valence (s) is +3.4, we show that the magnetic fluctuation exhibits strong layer-thickness dependence where it is enhanced at finite (zero) momentum in the thicker (thinner) layer system. A magnetic order phase appears sandwiched by two SC phases, consistent with the experiments. These two SC phases have different pairing states where one is the singlet extended s-wave state and the other is the triplet p-wave state. On the other hand, only a triplet p-wave SC phase with dome-shaped behavior of Tc is predicted when s=+3.5, which is also consistent with the experiments. Controversial experimental results on the magnetic properties are also discussed.Comment: 5 pages, 4 figures. Submitted to Journal of the Physical Society of Japa

Anisotropic Behavior of Knight Shift in Superconducting State of Na_xCoO_2yH_2O

The Co Knight shift was measured in an aligned powder sample of Na_xCoO_2yH_2O, which shows superconductivity at T_c \sim 4.6 K. The Knight-shift components parallel (K_c) and perpendicular to the c-axis (along the ab plane K_{ab}) were measured in both the normal and superconducting (SC) states. The temperature dependences of K_{ab} and K_c are scaled with the bulk susceptibility, which shows that the microscopic susceptibility deduced from the Knight shift is related to Co-3d spins. In the SC state, the Knight shift shows an anisotropic temperature dependence: K_{ab} decreases below 5 K, whereas K_c does not decrease within experimental accuracy. This result raises the possibility that spin-triplet superconductivity with the spin component of the pairs directed along the c-axis is realized in Na_xCoO_2yH_2O.Comment: 5 pages, 5 figures, to be published in Journal of Physical Society of Japan vol. 75, No.

Specific Heat and Superfluid Density for Possible Two Different Superconducting States in NaxCoO2.yH2O

Several thermodynamic measurements for the cobaltate superconductor, NaxCoO2.yH2O, have so far provided results inconsistent with each other. In order to solve the discrepancies, we microscopically calculate the temperature dependences of specific heat and superfluid density for this superconductor. We show that two distinct specific-heat data from Oeschler et al. and Jin et al. are reproduced, respectively, for the extended s-wave state and the p-wave state. Two different superfluid-density data are also reproduced for each case. These support our recent proposal of possible two different pairing states in this material. In addition, we discuss the experimentally proposed large residual Sommerfeld coefficient and extremely huge effective carrier mass.Comment: 5 pages, 4 figures, Submitted to J. Phys. Soc. Jp

Weak Magnetic Order in the Bilayered-hydrate Nax_{x}CoO2⋅y_{2}\cdot yH2_{2}O Structure Probed by Co Nuclear Quadrupole Resonance - Proposed Phase Diagram in Superconducting Nax_xCoO2⋅_{2} \cdot yyH2_2O

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 $\nu_Q$ correlates with magnetic fluctuations from measurements of NQR spectra and $1/T_1T$ in various samples. The higher-$\nu_Q$ 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 $\nu_Q$, 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.Comment: 5 pages, 6 figures, submitted to J. Phys. Soc. Jp