Strength of the Hubbard potential and its modification by breathing distortion in $\text{BaBiO}_{3}$

TL;DR

This paper investigates how electron-electron interactions influence the electronic structure of BaBiO3, revealing that these interactions significantly modify the electron-phonon coupling and may enable intermediate phases.

Contribution

The study provides an analytical expression for the screened Coulomb potential and assesses the impact of lattice distortions on the Hubbard potential in BaBiO3.

Findings

Electron-electron interactions lower the electron-phonon coupling in BaBiO3.

The magnitudes of Coulomb repulsion and phonon-mediated attraction are comparable.

Results suggest possible realization of intermediate phases in BaBiO3.

Abstract

$\text{BaBiO}_{3}$ compound is known as an archetype example of a three-dimensional Holstein model with the realization of the charge density wave state at half-filling and the superconducting state when doped. Although many works are devoted to the study of the electron-phonon interaction in $\text{BaBiO}_{3}$, the influence of the electron-electron Hubbard interaction on the electronic structure in this system is still under quest. In our work, we obtain an analytical expression for the screened Coulomb potential, and along with the basis of \textit{ab initio}-computed maximally localized Wannier orbitals, we quantitatively estimate the magnitude of the effective on-site Hubbard potential scrutinizing the effects of distortion of the crystal lattice. We show that a proper inclusion of the electron-electron interactions into the Holstein model significantly lowers the value of the underlying electron-phonon coupling. Finally, we find that the amplitudes of the repulsive electron-electron potential and its attractive counterpart mediated by the electron-phonon coupling are rather comparable. This may open a way for a realization of the intermediate phase of $\text{BaBiO}_{3}$ in terms of the Holstein-Hubbard model.