Oxygen holes and hybridization in the bismuthates

TL;DR

This study investigates the electronic structure of parent bismuth perovskites using ab initio and tight-binding methods, highlighting the role of Bi-$6s$ and O-$2p$ hybridization and modeling lattice distortion effects.

Contribution

It introduces a minimal tight-binding model based on DFT calculations that accurately describes bandstructure changes due to lattice distortions in ABiO$_{3}$ compounds.

Findings

Hybridization of Bi-$6s$ and O-$2p$ orbitals is crucial.

The model captures charge gap opening with breathing distortion.

A single extended molecular orbital model describes low-energy bands.

Abstract

Motivated by the recently renewed interest in the superconducting bismuth perovskites, we investigate the electronic structure of the parent compounds ABiO$_{3}$ (A= Sr, Ba) using $ab$ $initio$ methods and tight-binding (TB) modeling. We use the density functional theory (DFT) in the local density approximation (LDA) to understand the role of various interactions in shaping the ABiO$_{3}$ bandstructure near the Fermi level. It is established that interatomic hybridization involving Bi-$6s$ and O-$2p$ orbitals plays the most important role. Based on our DFT calculations, we derive a minimal TB model and demonstrate that it can describe the properties of the bandstructure as a function of lattice distortions, such as the opening of a charge gap with the onset of the breathing distortion and the associated condensation of holes onto $a_{1g}$-symmetric molecular orbitals formed by the O-$2p_{\sigma}$ orbitals on collapsed octahedra. We also derive a single band model involving the hopping of an extended molecular orbital involving both Bi-$6s$ and a linear combination of six O-$2p$ orbitals which provides a very good description of the dispersion and band gaps of the low energy scale bands straddling the chemical potential.