  Research on the oxide perovskites has uncovered electronic properties that
are strikingly enhanced compared with those in conventional metals. Examples
are the high critical temperatures of the cuprate superconductors and the
colossal magnetoresistance in the manganites. The conducting layered cobaltate
$\rm Na_xCoO_2$ displays several interesting electronic phases as $x$ is varied
including water-induced superconductivity and an insulating state that is
destroyed by field. Initial measurements showed that, in the as-grown
composition, $\rm Na_xCoO_2$ displays moderately large thermopower $S$ and
conductivity $\sigma$. However, the prospects for thermoelectric cooling
applications faded when the figure of merit $Z$ was found to be small at this
composition (0.6$<x<$0.7). Here we report that, in the poorly-explored
high-doping region $x>$0.75, $S$ undergoes an even steeper enhancement. At the
critical doping $x_p\sim$ 0.85, $Z$ (at 80 K) reaches values $\sim$40 times
larger than in the as-grown crystals. We discuss prospects for low-temperature
thermoelectric applications.
