  We investigated size effects on thermoelectricity in thin films of a strongly
correlated layered cobaltate. At room temperature, the thermopower is
independent of thickness down to 6 nm. This unusual behavior is inconsistent
with the Fuchs-Sondheimer theory, which is used to describe conventional metals
and semiconductors, and is attributed to the strong electron correlations in
this material. Although the resistivity increases, as expected, below a
critical thickness of $\sim$ 30 nm. The temperature dependent thermopower is
similar for different thicknesses but resistivity shows systematic changes with
thickness. Our experiments highlight the differences in thermoelectric behavior
of strongly correlated and uncorrelated systems when subjected to finite size
effects. We use the atomic limit Hubbard model at the high temperature limit to
explain our observations. These findings provide new insights on decoupling
electrical conductivity and thermopower in correlated systems.
