We present a relativistic symmetry analysis of the allowed pairing states in the noncentroymmetric superconductor LaNiC2. 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 nondegenerate pairing states with different critical temperatures. We address the breaking of time-reversal symmetry detected in recent muon spin-relaxation experiments and show that it is only compatible with such nonunitary 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
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