Does disorder destroy e$_{g'}$ pockets in Na$_{0.3}$CoO$_{2}$? A new ab initio method for disorder

Hydrated Na$_{0.3}$CoO$_{2}$ shows interesting superconductivity[1], with evidence of a nodal order parameter[2]. One possible origin of the nodal structure is {\it f}-wave pairing[3] due to the six e$_{g'}$ pockets predicted by the local density approximation[4]. However, ARPES experiments[5] showed no sign of these hole pockets. In this talk, we will investigate a recent proposal[6] of destruction of the e$_{g'}$ pockets due to disorder. An affordable {\it ab initio} Wannier function based method will be presented that takes into account spatial distributions of disorder, beyond existing mean-field approximations (e.g. VCA, CPA). We also use our Wannier functions to analyse the crystal field splitting, the sign of which critically determines the role of correlation in DMFT. \\[3pt] [1] K. Takada et al, Nature {\bf 422}, 53 (2003)\\[0pt] [2] Zheng G. et al, JPCM {\bf 18}, L63 (2006)\\[0pt] [3] Kuroki K. et al, PRL {\bf 93}, 077001-1 (2004)\\[0pt] [4] D. Singh, PRB {\bf 61}, 13397 (2000)\\[0pt] [5] Hasan M.Z. et al, PRL {\bf 92}, 246402 (2004)\\[0pt] [6] D. Singh et al PRL {\bf 97}, 016404 (2006)