Theory of sodium ordering in Na_xCoO₂

The ordering of Na ions in Na_xCoO₂ is investigated systematically by combining detailed density functional theory (DFT) studies with model calculations. Various ground state ordering patterns are identified, and they are in excellent agreement with available experimental results. Our results suggest that the primary driving force for the Na ordering is the screened Coulomb interaction among Na ions. Possible effects of the Na ordering on the electronic structure of the CoO₂ layer are discussed. We propose that the nonexistence of a charge ordered insulating state at x=2∕3 is due to the lack of a commensurate Na ordering pattern, whereas an extremely stable Na ordering at x=0.5 enhances the charge ordering tendency, resulting in an insulating state as observed experimentally.