Spin-Orbit Coupling and Symmetry of the Order Parameter in Strontium Ruthenate

TL;DR

This study investigates the stability of different superconducting states in Sr$_2$RuO$_4$, revealing that the chiral state is not energetically favored without spin-dependent pairing interactions, challenging previous assumptions about its stability.

Contribution

The paper demonstrates that the chiral superconducting state in Sr$_2$RuO$_4$ is not the minimum energy state when considering spin-orbit coupling, highlighting the need for spin-dependent pairing interactions.

Findings

Chiral state is never the minimum energy state with spin-orbit coupling.

Stability of the chiral state requires spin-dependent pairing interactions.

The chiral state has zero linear order effect from spin-orbit coupling.

Abstract

Determination of the orbital symmetry of a state in spin triplet Sr$_2$RuO$_4$ superconductor is a challenge of considerable importance. Most of the experiments show that the chiral state of the $\hat{z} (k_x \pm ik_y)$ type is realized and remains stable on lowering the temperature. Here we have studied the stability of various superconducting states of Sr$_2$RuO$_4$ in the presence of spin-orbit coupling. Numerically we found that the chiral state is never the minimum energy. Alone among the five states studied it has $<{\bf \hat L}.{\bf \hat S} >=0$ and is therefore not affected to linear order in the coupling parameter $\lambda$. We found that stability of the chiral state requires spin dependent pairing interactions. This imposes strong constraint on the pairing mechanism.