Phonon Fluctuations Enhanced Superconductivity in a Three-Band Cuprate Model

The microscopic origin of high-Tc superconductivity in cuprates remains an outstanding puzzle due to the interplay of intertwined orders. Experimental observations and theoretical studies have suggested crucial roles of phonons, with the B1g oxygen buckling mode emerging as a promising candidate. Here, we investigate the microscopic influence of this phonon in a three-band cuprate model. We find that the B1g phonon plays opposite roles in superconductivity depending on whether it lies in the adiabatic or antiadiabatic regime at a given temperature. Thermally populated adiabatic phonons suppress d-wave pairing through the loss of quasiparticle coherence, whereas antiadiabatic phonons simultaneously enhance coherence and the attractive d-wave pairing vertex, strengthening superconductivity across multiple diagnostics. This enhancement also exhibits pronounced electron-hole asymmetry arising from the different orbital characters of doped carriers. Our results therefore establish a microscopic mechanism through which B1g phonons can cooperate with electronic correlations to substantially enhance d-wave superconducting pairing in cuprates.