Disproportionation, Metal-Insulator Transition, and Critical Interaction Strength inNa1/2CoO2

Abstract

Charge disproportionation (CD) and spin differentiation in ${\mathrm{N}\mathrm{a}}_{1/2}{\mathrm{C}\mathrm{o}\mathrm{O}}_2$ are studied using the correlated band local-density approximation $+$ Hubbard U (LDA+U) approach. The simultaneous CD and gap opening seen previously is followed in detail through a first-order charge disproportionation transition $2{\mathrm{C}\mathrm{o}}^{3.5+}\to {\mathrm{C}\mathrm{o}}^{3+}+{\mathrm{C}\mathrm{o}}^{4+}$. Disproportionation in the Co $a_g$ orbital results in half of the ions (${\mathrm{C}\mathrm{o}}^{3+}$) becoming electronically and magnetically dead, transforming the quarter-filled $a_g$ system into a half-filled subsystem that subsequently undergoes the observed charge ordering or metal-insulator transition. Comparing with data in the $x\approx 0.3$ regime suggests the system has moved into the multiband regime where the effective Coulomb repulsion $U\to U_{\mathrm{e}\mathrm{f}\mathrm{f}}=U/\sqrt{3}$ strongly lessens correlation effects.