Possible pairing symmetries in SrPtAs with a local lack of inversion center

We discuss possible pairing symmetries in the hexagonal pnictide superconductor SrPtAs. The local lack of inversion symmetry of the two distinct conducting layers in the unit cell results in a special spin-orbit coupling with a staggered structure. We classify the pairing symmetry by the global crystal point group D3d, and suggest some candidates for the stable state using a tight-binding model with an in-plane, density-density type pairing interaction. We may have some unconventional states such as $s+f$ wave and a mixture of chiral d wave and chiral p wave. The spin-orbit coupling is larger than the interlayer hopping, and the mixing between spin-singlet and spin-triplet states can be seen in spite of the fact that the system has a global inversion center.