Theory of superconductivity in doped quantum paraelectrics

Recent experiments on Nb-doped SrTiO₃ have shown that the superconducting energy gap to the transition temperature ratio maintains the Bardeen–Cooper–Schrieffer (BCS) value throughout its superconducting dome. Motivated by these and related studies, we show that the Cooper pairing mediated by a single soft transverse-optical phonon is the most natural mechanism for such a superconducting dome given experimental constraints, and present the microscopic theory for this pairing mechanism. Furthermore, we show that this mechanism is consistent with the T² resistivity in the normal state. Lastly, we discuss what physical insights SrTiO₃ provides for superconductivity in other quantum paraelectrics such as KTaO₃.