Charge order and phonon renormalizations : Possible implications for cobaltates

Several experimental and theoretical studies in cobaltates suggest the proximity of the system to charge ordering (CO). We show, qualitatively, in the frame of a $t\text{\ensuremath{-}}V$ model coupled to phonons, that optical phonon modes at the $K$ and $M$ points of the Brillouin zone, which involves only O ions displacement around a Co ion, are good candidates to display anomalies due to the CO proximity. If by increasing of ${\mathrm{H}}_{2}\mathrm{O}$ content the system is pushed closer to CO, the mentioned phonon modes should show softening and broadening.