A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in BaBiO$_3$

TL;DR

This study uses nonperturbative hybrid Monte Carlo simulations to show that bond-stretching electron-phonon interactions are sufficient to induce charge-density-wave order in BaBiO₃, highlighting the importance of off-diagonal electron-phonon couplings.

Contribution

It introduces a comprehensive model including Bi and O orbitals and demonstrates the critical role of bond-stretching phonons in charge order formation in BaBiO₃.

Findings

Bond-stretching modes induce CDW transition

Small coupling strength suffices for charge order

Off-diagonal electron-phonon interactions are crucial

Abstract

The relationship between electron-phonon ($e$-ph) interactions and charge-density-wave (CDW) order in the bismuthate family of high-temperature superconductors remains unresolved. We address this question using nonperturbative hybrid Monte Carlo calculations for the parent compound BaBiO$_3$. Our model includes the Bi $6s$ and O $2p_\sigma$ orbitals and coupling to the Bi-O bond-stretching branch of optical phonons via modulations of the Bi-O hopping integral. We simulate three-dimensional clusters of up to 4000 orbitals, with input model parameters taken from {\it ab initio} electronic structure calculations and a phonon energy $\hbar\Omega_0 = 60$~meV. Our results demonstrate that the coupling to the bond-stretching modes is sufficient to reproduce the CDW transition in this system, despite a relatively small dimensionless coupling. We also find that the transition deviates from the weak-coupling Peierls' picture. This work demonstrates that off-diagonal $e$-ph interactions in orbital space are vital in establishing the bismuthate phase diagram.