Theory of superconductivity in doped quantum paraelectrics

TL;DR

This paper proposes a microscopic theory where Cooper pairing mediated by a soft transverse-optical phonon explains superconductivity in doped SrTiO$_3$, consistent with experimental observations including the BCS ratio and $T^2$ resistivity.

Contribution

It introduces a novel pairing mechanism mediated by a soft phonon in quantum paraelectrics, explaining the superconducting dome and normal state properties.

Findings

Superconducting gap to $T_c$ ratio remains BCS value throughout the dome.

The proposed phonon-mediated pairing explains the $T^2$ resistivity.

The theory applies to SrTiO$_3$ and offers insights into other quantum paraelectrics.

Abstract

Recent experiments on Nb-doped SrTiO$_3$ 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 $T^2$ resistivity in the normal state. Lastly, we discuss what physical insights SrTiO$_3$ provides for superconductivity in other quantum paraelectrics such as KTaO$_3$.