A $B_{1g}$ phonon unlocks $d$-wave superconductivity in the repulsive Hubbard model

Abstract

Using numerically exact finite-temperature quantum Monte Carlo, we demonstrate that a $B_{1g}$ phonon coupled to the doped $t$-$t'$ repulsive Hubbard model produces genuine $d$-wave superconductivity at a substantial transition temperature, in excess of either interaction alone. The observed trends suggest that stronger Hubbard repulsion may cooperate with the phonon to further raise the pairing scale. The enhancement persists at stronger repulsion within the accessible window, limited by the fermion sign problem, and follows a common trend across phonon frequencies $Ω$ when organized by a retardation scale $2πT/Ω$. We also find a well-defined superconducting dome in doping, echoing a characteristic feature of correlated superconductors. Our results identify the $B_{1g}$ phonon as a plausible microscopic ingredient for robust $d$-wave superconductivity in the Hubbard model and suggest a concrete, physically motivated route toward materials with higher superconducting transition temperatures.