Squaring the Triangle: Insulating Ground State of $Na_{0.5}CoO_{2}$

TL;DR

This paper investigates an insulating state in a triangular lattice Hubbard model at a specific filling, revealing charge order and antiferromagnetic properties that explain various experimental observations.

Contribution

It introduces a model with two sublattices at different fillings to explain the insulating and magnetic behavior of $Na_{0.5}CoO_{2}$.

Findings

Identification of a charge-ordered insulating state with specific lattice symmetry

Quantitative explanation of Hall coefficient sign change

Description of temperature-dependent resistivity and antiferromagnetic persistence

Abstract

We demonstrate that at a filling of $n=1.5$, an hexatic insulating state obtains in the extended Hubbard model on a triangular lattice. Composed of two tetragonal sublattices with fillings of $n=1$ and $n=2$, the insulating state is charge ordered and possesses an antiferromagnetic superlattice with dimension $a\times\sqrt{3}$. Two distinct energy scales arise in our model, a charge gap for the insulator and the effective exchange interaction in the antiferromagnet. Our model is capable of explaining both qualitatively and quantitatively the Hall coefficient including the sign change, the temperature dependence of the resistivity and the persistence of antiferromagnetism above the insulating state.