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.
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