Relativistic analysis of the pairing symmetry of the noncentrosymmetric superconductor LaNiC₂

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.