Chiral Superconductivity in UTe$_2$ via Emergent $C_4$ Symmetry and Spin Orbit Coupling

TL;DR

This paper proposes that emergent $C_4$ symmetry and spin-orbit coupling explain the near-degeneracy of superconducting components in UTe$_2$, leading to chiral triplet superconductivity with a specific order parameter.

Contribution

It introduces a new explanation for the near-degeneracy of superconducting components in UTe$_2$ based on emergent $C_4$ symmetry and spin-orbit coupling effects.

Findings

Emergent $C_4$ symmetry at the interaction level.

Superconducting order parameter belongs to 2D $E_u$ irrep.

Chiral order favored with spin-orbit coupling.

Abstract

A lot of attention has been drawn to superconductivity in UTe$_2$, with suggestions of time-reversal symmetry breaking triplet chiral superconducting order parameter. The chirality of the order parameter has been attributed to an accidental near degeneracy of two superconducting components belonging to 1D irreps $B_{2u}$ and $B_{3u}$ of the relevant $D_{2h}$ point group, and it has been argued that the chiral $B_{2u}+iB_{3u}$ combination is selected by ferromagnetic fluctuations. In this work we present a possible explanation of the near-degeneracy as a result of an accidental $C_4$ symmetry of the band structure, with the superconducting order parameter belonging the 2D $E_u$ irrep of $D_{4h}$ that uniquely descends to the sought after $B_{2u}+iB_{3u}$ combination. We show that the $C_4$ symmetry is emergent at the level of the interactions using a renormalization group calculation and argue that the chiral combination of the order parameter is favored when spin-orbit coupling is added to the model.