A review of some new perspectives on the theory of superconducting Sr$_2$RuO$_4$

TL;DR

This review explores new theoretical perspectives on the pairing symmetry and mechanisms in the unconventional superconductor Sr$_2$RuO$_4$, emphasizing the importance of 3D structures, chiral or complex pairings, and multiorbital effects.

Contribution

It highlights recent developments suggesting 3D pairing structures, chiral or mixed pairings for Kerr effects, and exotic multiorbital Cooper pairings in Sr$_2$RuO$_4$.

Findings

Pairing in $E_u$ symmetry has a 3D structure due to spin-orbit entanglement.

Superconductivity must be chiral or a complex mixture to explain Kerr effect.

Multiorbital descriptions reveal exotic pairing forms inaccessible in single-orbital models.

Abstract

The nature of the Cooper pairing in the paradigmatic unconventional superconductor Sr$_2$RuO$_4$ is an outstanding puzzle in condensed matter physics. Despite the tremendous efforts made in the past twenty-seven years, neither the pairing symmetry nor the underlying pairing mechanism in this material has been understood with clear consensus. This is largely due to the lack of a superconducting order that is capable of interpreting in a coherent manner the numerous essential experimental observations. At this stage, it may be desirable to reexamine the existing theoretical descriptions of superconducting Sr$_2$RuO$_4$. This review focuses on several recent developments that may provide some clues for future study. We highlight three separate aspects: 1) any pairing in the $E_u$ symmetry channel, with which the widely discussed chiral p-wave is associated, shall acquire a 3D structure due to spin-orbit entanglement; 2) if the reported Kerr effect is a superconductivity-induced intrinsic bulk response, the superconductivity must either exhibit a chiral character, or be complex mixtures of certain set of helical p-wave pairings; 3) when expressed in a multiorbital basis, the Cooper pairing could acquire numerous exotic forms that are inaccessible in single-orbital descriptions. The implications of each of these new perspectives are briefly discussed in connection with selected experimental phenomena.