Polaronic high-temperature superconductivity in optimally doped bismuthate Ba$_{0.63}$K$_{0.37}$BiO$_3$*

Magnetic measurements have been carried out in the superconducting and normal states of the optimally doped nonmagnetic bismuthate superconductor Ba$_{0.63}$ K$_{0.37}$ BiO$_3$. The magnetic data along with previous $\mu$SR, resistivity, and tunneling data consistently show that there is a large polaronic enhancement in the density of states and effective electron-phonon coupling constant. The first-principle calculation within the density-functional theory indicates a small electron-phonon coupling constant of about 0.3-0.4, which can only lead to about 1 K superconductivity within the conventional phonon-mediated mechanism. Remarkably, the polaronic effect increases the electron-phonon coupling constant to about 1.4, which is large enough to lead to 32 K superconductivity. The present work thus uncovers the mystery of high-temperature superconductivity in bismuthate superconductors, which will also provide important insight into the pairing mechanism of other high-temperature superconductors.