Fermi surface evolution and Luttinger theorem in Na$_x$CoO$_2$: a systematic photoemission study

We report a systematic angle-resolved photoemission study on Na$_x$CoO$_2$ for a wide range of Na concentrations ($0.3 \leq x \leq 0.72$). In all the metallic samples at different $x$, we observed (i) only a single hole-like Fermi surface centered around $\Gamma$ and (ii) its area changes with $x$ according to the Luttinger theorem. We also observed a surface state that exhibits a larger Fermi surface area. The $e_g^\prime$ band and the associated small Fermi surface pockets near the $K$ points predicted by band calculations are found to ``sink'' below the Fermi energy in a manner almost independent of the doping and temperature.