Topological Properties of Time Reversal Symmetric Kitaev Chain and Applications to Organic Superconductors

TL;DR

This paper demonstrates the topological robustness of Majorana modes in a 1D spin triplet superconductor, with implications for organic superconductors, showing stability against various perturbations including time reversal symmetry breaking.

Contribution

It reveals that the Majorana modes in a 1D triplet superconductor are topologically protected due to a hidden chiral symmetry, classifying the system in the BDI topological class with an integer invariant.

Findings

Majorana modes are robust to disorder and certain perturbations.

The system belongs to the BDI topological class with an integer Z invariant.

Implications for organic superconductors like Bechgaard salts.

Abstract

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.