Textured electronic states of the triangular-lattice Hubbard model and NaxCoO2

We show that geometric frustration and strong correlation in the triangular-lattice Hubbard model lead a rich phase structure of root 3 x root 3 spin-charge textured electronic states over a wide region of electron doping 0 <= x <= 0.40. In addition to the 120 degrees Neel ordered insulator at half filling, we found a spin charge ordered insulator at x = 1/3 with collinear antiferromagnetic (AF) order on the underlying unfrustrated honeycomb lattice. Separating the two insulating phases is a Lifshitz transition between a noncollinear AF ordered metal and one with coexisting charge order. We obtain the phase diagram and the evolution of the Fermi surface (FS). Remarkably, the correlated ground states near x = 1/3 emerge as doping the 1/3 AF insulator by excess carriers, leading to electron and hole FS pockets with important implications for the cobaltate superconducting state.