Reconciling $\pi$ phase shift in Josephson junction experiments with even-parity superconductivity in Sr$_2$RuO$_4$

TL;DR

This paper proposes that an even-parity pseudospin-singlet state with interorbital pairing and spin-orbit coupling can explain experimental results in Sr$_2$RuO$_4$, reconciling previous conflicting evidence about its pairing symmetry.

Contribution

It introduces a novel explanation for Sr$_2$RuO$_4$'s pairing symmetry, showing how even-parity states can mimic odd-parity characteristics in experiments.

Findings

Interorbital pairing with spin-orbit coupling explains experimental data.

Mirror symmetry breaking allows even-parity states to exhibit odd-parity features.

Proposes experimental methods to distinguish pairing states.

Abstract

The superconducting state of Sr$_2$RuO$_4$ was once thought to be a leading candidate for $p$-wave superconductivity. A constant Knight shift below the transition temperature provided evidence for spin-triplet pairing, and a $\pi$ phase shift observed in Josephson junction tunneling experiments suggested odd-parity pairing, both of which are described by $p$-wave states. However, with recent experiments observing a significant decrease in the Knight shift below the transition temperature, signifying a spin-singlet state, the odd-parity results are left to be reconciled. In this work, we show that an even-parity pseudospin-singlet state originating from interorbital pairing via spin-orbit coupling can explain what has been assumed to be evidence for an odd-parity state. In the presence of small mirror symmetry breaking, interorbital pairing is uniquely capable of displaying odd-parity characteristics required to explain these experimental results. Further, we discuss how these experiments may be used to differentiate the proposed pairing states of Sr$_2$RuO$_4$.