Noncentrosymmetric superconductors in one dimension

TL;DR

This paper investigates boundary modes in one-dimensional noncentrosymmetric superconductors with spin-orbit coupling, revealing conditions for zero-energy states based on band gap sign differences.

Contribution

It demonstrates that in 1D superconductors with broken inversion symmetry, only an s-wave-like pairing symmetry exists and identifies when zero-energy boundary states occur.

Findings

Zero-energy bound states depend on sign differences of the gap function across bands.

Only one pairing symmetry, analogous to s-wave, is possible in 1D noncentrosymmetric superconductors.

Boundary states are present if an odd number of bands have a different gap sign.

Abstract

We study the fermionic boundary modes (Andreev bound states) in a time-reversal invariant one-dimensional superconductor. In the presence of a substrate, spatial inversion symmetry is broken and the electronic properties are strongly affected by an antisymmetric spin-orbit coupling. We assume an arbitrary even number of nondegenerate bands crossing the Fermi level. We show that there is only one possible pairing symmetry in one dimension, an analog of s-wave pairing. The zero-energy Andreev bound states are present if the sign of the gap function in an odd number of bands is different from all other bands.