Correlation-enhanced electron-phonon coupling and superconductivity in (Ba,K)SbO$_3$ superconductors

The electronic structure, lattice dynamics, and electron-phonon coupling (EPC) of the newly discovered (Ba,K)SbO$_3$ superconductors are investigated by first-principles calculations. The EPC of (Ba,K)SbO$_3$ is significantly enhanced by considering non-local electronic correlation using the Heyd-Scuseria-Ernzerhof hybrid exchange-correlation functional (HSE06). The EPC strength {\lambda} of Ba$_{0.35}$K$_{0.65}$SbO$_3$ is strongly increased from 0.33 in local-density approximation calculations to 0.59 in HSE06 calculations, resulting in a superconducting transition temperature Tc of about 14.9 K, which is in excellent agreement with experimental value of ~ 15 K. Our findings suggest (Ba,K)SbO$_3$ are extraordinary conventional superconductors, where non-local electronic correlation expands the bandwidth, enhances the EPC, and boosts the Tc. Moreover, we find both {\lambda} and Tc depend crucially on the K-doping level for (Ba,K)SbO$_3$ and (Ba,K)SbO$_3$ compounds. (Ba,K)SbO$_3$ have stronger EPC strength and higher Tc than those of (Ba,K)SbO$_3$ at the same K-doping level.