Relativistic analysis of the pairing symmetry of the noncentrosymmetric superconductor LaNiC$_2$

TL;DR

This paper analyzes the symmetry of pairing states in LaNiC$_2$, showing how spin-orbit coupling influences pairing symmetry and explaining experimental observations of time-reversal symmetry breaking.

Contribution

It provides a relativistic symmetry analysis of pairing states in LaNiC$_2$, highlighting the role of spin-orbit coupling and identifying non-unitary triplet pairing as consistent with experiments.

Findings

SOC splits triplet pairing states into non-degenerate states with different T_c

Time-reversal symmetry breaking is compatible with non-unitary triplet pairing

Conventional singlet pairing with small triplet admixture is inconsistent with data

Abstract

We present a relativistic symmetry analysis of the allowed pairing states in the noncentroymmetric superconductor LaNiC$_2$. The case of zero spin-orbit coupling (SOC) is discussed first and then the evolution of the symmetry-allowed superconducting instabilities as SOC is adiabatically turned on is described. In addition to mixing singlet with triplet pairing, SOC splits some triplet pairing states with degenerate order parameter spaces into non-degenerate pairing states with different critical temperatures. We address the breaking of time-reversal symmetry (TRS) detected in recent muon spin relaxation experiments and show that it is only compatible with such non-unitary triplet pairing states. In particular, an alternative scenario featuring conventional singlet pairing with a small admixture of triplet pairing is shown to be incompatible with the experimental data.