  We study a three-orbital Su-Schrieffer-Heeger model defined on a
two-dimensional Lieb lattice and in the negative charge transfer regime using
determinant quantum Monte Carlo. At half-filling (1 hole/unit cell), we observe
a bipolaron insulating phase, where the ligand oxygen atoms collapse and expand
about alternating cation atoms to produce a bond-disproportionated state. This
phase is robust against moderate hole doping but is eventually suppressed at
large hole concentrations, leading to a metallic polaron-liquid-like state with
fluctuating patches of local distortions. Our results suggest that the polarons
are highly disordered in the metallic state and freeze into a periodic array
across the metal-to-insulator transition. We also find an $s$-wave
superconducting state at finite doping that primarily appears on the oxygen
sublattices. Our approach provides an efficient, non-perturbative way to treat
bond phonons in higher dimensions and our results have implications for many
materials where coupling to bond phonons is the dominant interaction.

Materials Science;Superconductivity