Formation of non-unitary state near the upper-critical field of Sr$_2$RuO$_4$

TL;DR

This paper investigates the superconducting state of Sr$_2$RuO$_4$ under a magnetic field, revealing a transition from a non-unitary to a unitary state near the upper critical field, explaining specific heat anomalies.

Contribution

It demonstrates the formation of a non-unitary superconducting state near H$_{c2}$ due to weak spin-orbit coupling, a novel insight into Sr$_2$RuO$_4$'s behavior.

Findings

Non-unitary state forms at H$_{c2}$ due to weak spin-orbit coupling.

Transition from non-unitary to unitary state as magnetic field decreases.

Explains double peaks in specific heat and their disappearance at low fields.

Abstract

We have studied the superconducting state of Sr$_2$RuO$_4$ under a magnetic field parallel to the superconducting plane. We show that due to a weak spin-orbit coupling, non-unitary k$_y(\hat{\mathbf{z}}-i\alpha\hat{\mathbf{y}})$ state is formed right at H$_{c2}$, then changes to unitary k$_y\hat{\mathbf{z}}$ state, as a magnetic field is lowered. In terms of this crossover, we address the origin of the observed double peaks of specific heat and the disappearance of the double peaks at low fields.