$\mu$SR study of unconventional pairing symmetry in the quasi-1D Na${}_2$Cr${}_3$As${}_3$ superconductor

We report the finding of a novel pairing state in a newly discovered superconductor Na${}_2$Cr${}_3$As${}_3$. This material has a noncentrosymmetric quasi-one-dimensional crystal structure and is superconducting at $T_{\mathrm{C}}\sim$ 8.0 K. We find that the magnetic penetration depth data suggests the presence of a nodal line $p_z$-wave pairing state with zero magnetic moment using transverse-field muon-spin rotation (TF-$\mu$SR) measurements. The nodal gap observed in Na${}_2$Cr${}_3$As${}_3$ compound is consistent with that observed in isostructural (K,Cs)${}_2$Cr${}_3$As${}_3$ compounds using TF-$\mu$SR measurements. The observed pairing state is consistent with a three-band model spin-fluctuation calculation, which reveals the $S_z=0$ spin-triplet pairing state with the $\sin k_z$ pairing symmetry. The long-sought search for chiral superconductivity with topological applications could be aided by such a novel triplet $S_z=0$ $p$-wave pairing state.