Possibility of chiral $d$-wave state in the hexagonal pnictide superconductor SrPtAs

We discuss the type of pairing in the hexagonal pnictide superconductor SrPtAs, taking into account its multiband structure. The topological chiral $d$-wave state with time-reversal-symmetry breaking has been anticipated from the spontaneous magnetization observed by the muon-spin-relaxation experiment. We point out in this paper that the recent experimental reports on the nuclear-spin-lattice relaxation rate $T_1^{-1}$ and superfluid density $n_s(T)$, which seemingly support the conventional $s$-wave pairing, are also consistent with the chiral $d$-wave state. The compatibility of the gap and multiband structures is crucial in this argument.