Electron-phonon interaction dressed by electronic correlations near charge ordering. Possible implications for cobaltates

We consider possible routes to superconductivity on the basis of the t-J-V model plus phonons on the triangular lattice. We studied the stability conditions for the homogeneous Fermi liquid (HFL) phase against different broken symmetry phases. Besides the root 3 x root 3 CDW phase, triggered by the nearest-neighbour Coulomb interaction V, we have found that the HFL is unstable, at very low doping, against a bond-ordered phase due to J. We also discuss the occurrence of phase separation at low doping and V. The interplay between the electron-phonon interaction and correlations near the root 3 x root 3 CDW leads to superconductivity in the unconventional next-nearest-neighbour f-wave (NNN-f) channel with a dome shape for T-c around x similar to 0.35, and with values of a few kelvin. Near the bond-ordered phase at low doping we found tendencies to superconductivity with d-wave symmetry for finite J and x < 0.15. Possible implications for cobaltates are discussed.