Topological Properties of 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 total Cooper pair spin S_x=0 (i.e., Delta_{up,up} = -Delta_{down,down} = p*Delta_0; two uncoupled time reversed copies of the Kitaev p-wave chain) are topologically robust to perturbations such as mixing by the S_z=0 component of the order parameter (Delta_{up,down}=Delta_{down,up}), transverse hopping (in quasi-1D systems), non-magnetic disorder, and also, most importantly, to time reversal breaking perturbations such as applied Zeeman fields/magnetic impurities and the mixing by the S_y=0 component of the triplet order parameter (Delta_{up,up}=Delta_{down,down}). We show that the robustness to time reversal breaking results from a hidden chiral symmetry which places the system in the BDI topological class with an integer Z invariant. Our work has important implications for the quasi-1D organic superconductors (TMTSF)_2X (X=PF_6, CIO_4) (Bechgaard salts) which have been proposed as triplet superconductors with equal spin pairing (Delta_{up,up},Delta_{down,down} \neq 0, Delta_{up,down}=0) in applied magnetic fields.