Relativistic analysis of the pairing symmetry of the noncentrosymmetric superconductor ${\text{LaNiC}}_2$

We present a relativistic symmetry analysis of the allowed pairing states in the noncentroymmetric superconductor ${\text{LaNiC}}_2$. 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 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.

Figure 1

Evolution of all the superconducting instabilities of the normal state of ${\text{LaNiC}}_2$ allowed by symmetry in the absence of SOC as the latter is adiabatically turned on: (a) singlet pairing instabilities; (b) unitary triplet pairing instabilities; and (c) nonunitary triplet pairing instabilities. The relative temperatures of the different instabilities in this diagram are arbitrary.

Figure 2

(Color online) Venn-Euler diagram showing how the four pairing states allowed just below $T_c$ in the presence of spin-orbit coupling decompose into the 12 singlet, nonunitary triplet, and unitary triplet states allowed in its absence.