Renormalization of Coulomb interactions in s-wave superconductor Na${}_x$CoO${}_2$

Abstract

We study the renormalized Coulomb interactions due to retardation effect in Na${}_x$CoO${}_2$. Although the Morel-Anderson's pseudo potential for $a_{1g}$ orbital ${\mu }_{a1g}^{\ast }$ is relatively large because the direct Coulomb repulsion $U$ is large, that for interband transition between $a_{1g}$ and $e_g^{\prime }$ orbitals ${\mu }_{a1g,e{g}^{\prime }}^{\ast }$ is very small since the renormalization factor for pair hopping $J$ is square of that for $U$. Therefore, the s-wave superconductivity due to valence-band Suhl-Kondo mechanism will survive against strong Coulomb interactions. The interband hopping of Cooper pairs due to shear phonons is essential to understand the superconductivity in Na${}_x$CoO${}_2$.

2pages, 2figures, Proceedings of ICM in Kyoto, 2006