Bipolaron insulators and polaron liquids in high-temperature superconductors Ba_1-xK_xBiO₃

The Su-Schrieffer-Heeger (SSH) type electron-phonon (e-ph) coupling, arising from the modulation of the atomic overlap integrals, has been proposed as a driving mechanism formation of an insulating state in the high-temperature superconducting bismuthates Ba_1-xK_xBiO₃. However, this e-ph interaction has not been well studied in dimensions greater than one due to a lack of suitable numerical techniques. In this talk, we present a determinant quantum Monte Carlo (DQMC) method for simulating the SSH-type e-ph interaction in a three-orbital model defined on a two-dimensional Lieb lattice. At half-filling, we observe a bipolaron insulating phase characterized by a long-range dimerized distortion, where the ligand oxygens collapse and expand about alternating Bi atoms creating a bond-disproportionated state. This state 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 dimerized distortions. Our result suggests that the polarons are highly disordered in the metallic state and freeze into a periodic array across the metal-to-insulator transition. Moreover, our results have broad implications for many perovskite materials, where the bond phonons are essential.