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

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 $\hslash {\Omega }_0=60$~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.

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