Superconductivity in non-centrosymmetric LaNiC2

We present a discussion of superconductivity in non-centrosymmetric superconductors with spin-orbit coupling. A general expression for the quasiparticle excitation energy is derived. The superconducting states for the point group C2v are classified by symmetry in the limit of weak spin-orbit coupling. A non-unitary triplet pairing gap function can account for observations of broken time-reversal symmetry and nodes in the superconducting state of LaNiC2; however such a gap function also has a gapless branch and requires vanishing spin-orbit coupling.