Cooperative orbital ordering and Peierls instability in the checkerboard lattice with doubly degenerate orbitals

TL;DR

This paper investigates theoretically how orbital ordering and electron-phonon interactions can lead to Peierls instabilities and bond dimerization in a simplified checkerboard lattice model with doubly degenerate orbitals, relevant to spinel materials.

Contribution

It introduces a theoretical model demonstrating the formation of orbitally-driven Peierls states and bond dimerization, highlighting conditions under which these phenomena occur or are suppressed.

Findings

Stable orbitally-induced Peierls bond-dimerized state at one electron per atom.

Peierls distortion persists even with reduced orbital charge density.

Peierls instability is absent at half electron per atom density in the model.

Abstract

It has been suggested that the metal-insulator transitions in a number of spinel materials with partially-filled t_2g d-orbitals can be explained as orbitally-driven Peierls instabilities. Motivated by these suggestions, we examine theoretically the possibility of formation of such orbitally-driven states within a simplified theoretical model, a two-dimensional checkerboard lattice with two directional metal orbitals per atomic site. We include orbital ordering and inter-atom electron-phonon interactions self-consistently within a semi-classical approximation, and onsite intra- and inter-orbital electron-electron interactions at the Hartree-Fock level. We find a stable, orbitally-induced Peierls bond-dimerized state for carrier concentration of one electron per atom. The Peierls bond distortion pattern continues to be period 2 bond-dimerization even when the charge density in the orbitals forming the one-dimensional band is significantly smaller than 1. In contrast, for carrier density of half an electron per atom the Peierls instability is absent within one-electron theory as well as mean-field theory of electron-electron interactions, even for nearly complete orbital ordering. We discuss the implications of our results in relation to complex charge, bond, and orbital-ordering found in spinels.