Theory of the carrier concentration-dependent behavior in layered cobaltates

Layered cobaltates -- anhydrous Na$_x$CoO$_2$, Li$_x$CoO$_2$ and the ``misfit'' cobaltates [Bi$_2$A$_2$O$_4$] $\cdot$ [CoO$_2$]$_m$, where A = Ba, Sr or Ca -- have attracted wide attention for their 2D layered structure and metallicity (both reminescent of 2D cuprates), and the tunability of the carrier concentration over a wide range. The Co ions form a 2D triangular lattice, and their formal charge in Na$_x$CoO$_2$ and Li$_x$CoO$_2$ can be tuned from Co$^{3+}$ at $x=1$ to Co$^{4+}$ at $x=0$. Charge carriers in all cases are holes, with the carrier concentration given by the fraction of Co-ions that are in the S = 1/2 Co$^{4+}$ state. Experiments have indicated remarkable carrier concentration dependent magnetic susceptibility and thermoelectric power that remains unexplained to date. Specifically, all three systems show weakly correlated behavior at small nonzero $x$ (large carrier concentration), and strongly correlated behavior at large $x$ (small carrier concentration). In this talk we give clear theoretical explanation of the observed carrier concentration dependence within an $a_{1g}$-only one-band extended Hubbard Hamiltonian. The key to understanding the $x$-dependence is to have realistic finite on-site correlation $U$ and significant intersite Coulomb interaction $V$. We present exact numerical results for triangular lattices upto 20 sites, and make detailed comparisons to experiments.