Electron-Phonon mechanism for Superconductivity in Na${}_{0.35}$CoO${}_2$: 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 $t_{2g}(a_{1g}+e_g^{\mathrm{\prime }})$-electrons of Co-ions, and study the transition temperature for a s-wave superconductivity. The obtained $T_{\rm c}$isverylowwhenthe$e_g’$-valence-bands are far below the Fermi level. However, $T_{\mathrm{c}}$ is strongly enhanced when the top of the $e_g^{\mathrm{\prime }}$-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 ($m^{\ast }\mathrm{/}m\sim 3$) due to optical phonons, is also explained.