59Co-NQR study on superconducting NaxCoO2.yH2O

Layered Co oxide NaxCoO2.yH2O with a superconducting transition temperature Tc =4.5 K has been studied by 59Co NQR. The nuclear spin relaxation rate 1/59T1 is nearly proportional to temperature T in the normal state. In the superconducting state, it exhibits the coherence peak and decreases with decreasing T below ~0.8Tc. Detailed comparison of the 1/T1T values and the magnetic susceptibilities between NaxCoO2.yH2O and NaxCoO2 implies that the metallic state of the former system is closer to a ferromagnetic phase than that of the latter. These experimental results impose a restriction on the mechanism of the superconductivity.Comment: 7 pages, 5 figures. to be published in J. Phys. Soc. Jpn. 72 (2003) No.

Novel phase diagram of superconductor NaxCoO2-yH2O in a 75 % relative humidity

We succeeded in synthesizing the powder samples of bilayer-hydrate sodium cobalt oxide superconductors NaxCoO2-yH2O with Tc = 0 ~ 4.6 K by systematically changing the keeping duration in a 75 % relative humidity atmosphere after intercalation of water molecules. From the magnetic measurements, we found that the one-day duration sample does not show any superconductivity down to 1.8 K, and that the samples kept for 2 ~ 7 days show superconductivity, in which Tc increases up to 4.6 K with increasing the duration. Tc and the superconducting volume fraction are almost invariant between 7 days and 1month duration. The 59Co NQR spectra indicate a systematic change in the local charge distribution on the CoO2 plane with change in duration.Comment: 4 pages, 5 figures, submitted to Journal of the Physical Society of Japa

Combinatorial sieves of dimension exceeding one

AbstractA general sieve for each dimension κ > 1 is given which improves the sieve estimates of Ankeny and Onishi. The work depends on a combinatorial identity which is invariant under Buchstab iteration and on the solution of a pair of differential-difference equations with side conditions

On the ratio of consecutive gaps between primes

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively

Oscillations of the F(R) dark energy in the accelerating universe

Oscillations of the $F(R)$ dark energy around the phantom divide line, $\omega_{DE}=-1$, both during the matter era and also in the de Sitter epoch are investigated. The analysis during the de Sitter epoch is revisited by expanding the modified equations of motion around the de Sitter solution. Then, during the matter epoch, the time dependence of the dark energy perturbations is discussed by using two different local expansions. For high values of the red shift, the matter epoch is a stable point of the theory, giving the possibility to expand the $F(R)$-functions in terms of the dark energy perturbations. In the late-time matter era, the realistic case is considered where dark energy tends to a constant. The results obtained are confirmed by precise numerical computation on a specific model of exponential gravity. A novel and very detailed discussion is provided on the critical points in the matter era and on the relation of the oscillations with possible singularities.Comment: 23 pages, 11 figures, version to appear in EPJ

Structure and Dynamics of Superconducting NaxCoO(2) Hydrate and Its Unhydrated Analog

Neutron scattering has been used to investigate the crystal structure and lattice dynamics of superconducting Na0.3CoO2 1.4(H/D)2O, and the parent Na0.3CoO2 material. The structure of Na0.3CoO2 consists of alternate layers of CoO2 and Na and is the same as the structure at higher Na concentrations. For the superconductor, the water forms two additional layers between the Na and CoO2, increasing the c-axis lattice parameter of the hexagonal P63/mmc space group from 11.16 A to 19.5 A. The Na ions are found to occupy a different configuration from the parent compound, while the water forms a structure that replicates the structure of ice. Both types of sites are only partially occupied. The CoO2 layer in these structures is robust, on the other hand, and we find a strong inverse correlation between the CoO2 layer thickness and the superconducting transition temperature (TC increases with decreasing thickness). The phonon density-of-states for Na0.3CoO2 exhibits distinct acoustic and optic bands, with a high-energy cutoff of ~100 meV. The lattice dynamical scattering for the superconductor is dominated by the hydrogen modes, with librational and bending modes that are quite similar to ice, supporting the structural model that the water intercalates and forms ice-like layers in the superconductor.Comment: 14 pages, 7 figures, Phys. Rev. B (in press). Minor changes + two figures removed as requested by refere

Unconventional magnetic transition and transport behavior in Na0.75CoO2

Here we report an unconventional magnetic and transport phenomenon in a layered cobalt oxide, NaxCoO2. Only for x = 0.75, a magnetic transition of the second order was clearly detected at Tm ~ 22 K where an apparent specific-heat jump, an onset of extremely small spontaneous magnetization, and a kink in resistivity came in. Moreover large positive magnetoresistance effect was observed below Tm. These features of the transition strongly indicate the appearance of an unusual electronic state that may be attributed to the strongly-correlated electrons in Na0.75CoO2.Comment: 5 pages, 6 figures, to appear in Phys. Rev.

Origin of the Superconductivity in the Y-Sr-Ru-O and Y-Sr-Cu-O Systems

We report on the structural, magnetic, and Raman-scattering studies of double perovskite structure Sr2Y(Ru1-xCux)O6-d systems made by systematic synthesis processes with various numbers of doping concentrations and sintering temperatures. We observed different behaviors resulting from the different thermal treatments. In particular, superconductivity in Cu-doped Sr2YRuO6 has been observed only for partially melted ceramic materials. We show that superconductivity is associated with the 1:2:3 phase (YSr2Cu3Ot), similar to that of Y-Sr-Cu-O samples sintered at high temperature

Future cosmological evolution in f(R)f(R) gravity using two equations of state parameters

We investigate the issues of future oscillations around the phantom divide for $f(R)$ gravity. For this purpose, we introduce two types of energy density and pressure arisen from the $f(R)$-higher order curvature terms. One has the conventional energy density and pressure even in the beginning of the Jordan frame, whose continuity equation provides the native equation of state $w_{\rm DE}$. On the other hand, the other has the different forms of energy density and pressure which do not obviously satisfy the continuity equation. This needs to introduce the effective equation of state $w_{\rm eff}$ to describe the $f(R)$-fluid, in addition to the native equation of state $\tilde{w}_{\rm DE}$. We confirm that future oscillations around the phantom divide occur in $f(R)$ gravities by introducing two types of equations of state. Finally, we point out that the singularity appears ar $x=x_c$ because the stability condition of $f(R)$ gravity violates.Comment: 23 pages, 10 figures, correcting typing mistake in titl

A new approach to cosmological perturbations in f(R) models

We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given f(R) modified gravity model and a LCDM reference model. Our method allows to study structure formation in these models from the largest scales, of the order of the Hubble horizon, down to scales deeply inside the Hubble radius, without employing the so-called "quasi-static" approximation. Although we restrict our analysis here to linear perturbations, our technique is completely general and can be extended to any perturbative order.Comment: 21 pages, 2 figures; Revised version according to reviewer's suggestions; Typos corrected; Added Reference