Superconducting pairing in Sr$_2$RuO$_4$ from weak to intermediate coupling

TL;DR

This study investigates the superconducting pairing mechanisms in Sr$_2$RuO$_4$, revealing a transition from p-wave to anisotropic even-parity pairing as interaction strength increases, considering spin-orbit effects.

Contribution

It provides a systematic microscopic analysis of pairing instabilities in Sr$_2$RuO$_4$ accounting for spin-orbit coupling, highlighting the dominance of different pairing symmetries across interaction regimes.

Findings

P-wave pairing favored at very weak interactions.

Highly anisotropic even-parity pairings dominate at stronger interactions.

Results offer insights into the complex superconductivity of Sr$_2$RuO$_4$.

Abstract

The unconventional superconductivity in Sr$_2$RuO$_4$ continues to attract considerable interest. While many measurements can be interpreted on the basis of chiral $p$-wave pairing with intriguing topological character, a number of exceptions hinder an unambiguous verification of such pairing. The pairing mechanism also remains under debate. In this paper, with effects of the sizable spin-orbit coupling accounted for, we reexamine the superconducting instabilities in Sr$_2$RuO$_4$ through systematic microscopic analysis within random phase approximation. Our calculations show that the odd-parity $p$-wave pairing is favored in the regime of extremely weak interactions, but that highly anisotropic even-parity pairings become most leading over a broad range of stronger interactions. These results could shed light on the nature of the enigmatic superconductivity in Sr$_2$RuO$_4$.