Topological properties of the time-reversal-symmetric Kitaev chain and applications to organic superconductors

We show that the pair of Majorana modes at each end of a 1D spin triplet superconductor with Δ↑↑=-Δ↓↓=pΔ0 (two time reversed copies of the Kitaev p-wave chain) are topologically robust to perturbations such as mixing by the Sz=0 component of the order parameter (Δ↑↓=Δ↓↑), transverse hopping, nonagnetic disorder, and also, importantly, to time-reversal (TR) breaking perturbations such as applied Zeeman fields/magnetic impurities and the mixing by the Sy=0 component of the order parameter (Δ↑↑=Δ↓↓). We show that the robustness to TR-breaking results from a hidden chiral symmetry, which places the system in the BDI class in the presence of the generic TR-breaking perturbations (the TR-invariant system is both DIII and BDI). Our work has important implications for the quasi-1D organic superconductors (TMTSF)2X (X=PF6, CIO4) (Bechgaard salts) and Li0.9Mo6O17, which have been proposed as triplet superconductors with equal spin pairing (Δ↑↑ ,Δ↓↓≠0,Δ↑↓=0) in the presence of magnetic fields.