Phonon softening in ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2\bullet y{\mathrm{H}}_2\mathrm{O}$: Implications for the Fermi surface topology and the superconducting state

In this work we investigate the relevance of phonons for the superconductivity in ${\mathrm{Na}}_{0.35}\mathrm{Co}{\mathrm{O}}_2\bullet 1.3{\mathrm{H}}_2\mathrm{O}$. We measure phonon dispersion in this material as well as in the nonhydrated parent compound ${\mathrm{Na}}_{0.7}\mathrm{Co}{\mathrm{O}}_2$ by inelastic x-ray scattering. The measured phonon dispersion along the $\Gamma \text{−}M$ direction shows a marked softening of Co-related optical phonon branches close to the Brillouin zone boundary, with hole doping. The phonon spectra, dispersion, and softening of Co-vibration modes are well reproduced by first-principles calculations. The critical temperature estimated from a phonon-mediated mechanism is much lower than the measured one, suggesting a nonconventional superconducting state in this material.

Figure 1

(Color online) IXS spectra in nonhydrated and hydrated compounds measured along the $\Gamma \text{−}M$ direction (circles). The measurements are compared to ab initio calculations of the dynamical structure factor (solid lines). The calculated spectra are shown for Na occupying sites $2b$ and $2d$. The main dispersive feature is indicated by arrows.

Figure 2

(Color online) (a)–(d) Measured (open symbols) and calculated (lines) phonon dispersion along high-symmetry directions in model NCOH and NCO compounds (see text for details). The structure factor intensity is indicated in normalized unit by the gray scale from black (1) to light gray $\left({10}^{-6}\right)$ and below ${10}^{-6}$ as dotted lines. Raman and infrared data are borrowed from Ref. 22. Adjacent panels: projected phonon density of states.