Disproportionation and Critical Interaction Strength in Na$_x$CoO$_2$: Concentration Dependence

TL;DR

This study investigates how charge disproportionation and magnetic properties in Na$_x$CoO$_2$ depend on sodium concentration, revealing a phase diagram influenced by Coulomb interactions and structural factors.

Contribution

It introduces a concentration-dependent Coulomb U and a phase diagram for Na$_x$CoO$_2$ based on first-principles calculations, linking structural and electronic properties.

Findings

Charge disproportionation occurs via a first-order transition.

The Coulomb U varies significantly with sodium concentration.

A phase diagram correlates U, charge order, and structural effects.

Abstract

We present results of studies of charge disproportionation (CD) and spin differentiation in Na$_x$CoO$_2$ using the correlated band theory approach (local-density approximation+Hubbard U:LDA+U). The simultaneous CD and gap opening can be followed through a first order charge disproportionation transition. By comparison with experiments, we propose a value of the Coulomb repulsion strength U($x$) that has significant dependence on the carrier concentration $x$, for which we obtain a phase diagram. The connection between the oxygen height and effects of on-site correlation is also reported.