Topological superconducting phase in helical Shiba chains

TL;DR

This paper theoretically investigates topological superconductivity and Majorana states in helical Shiba chains, highlighting the effects of long-range interactions and complex hopping on the phase diagram and state localization.

Contribution

It develops a detailed tight-binding Bogoliubov-de Gennes model for Shiba chains, revealing key differences from the Kitaev model and analyzing their impact on topological phases.

Findings

Identification of conditions for topological phase in Shiba chains

Analysis of long-range hopping effects on Majorana states

Numerical confirmation of phase diagram predictions

Abstract

Recently, it has been suggested that topological superconductivity and Majorana end states can be realized in a chain of magnetic impurities on the surface of an s-wave superconductor when the magnetic moments form a spin helix as a result of the RKKY interaction mediated by the superconducting substrate. Here, we investigate this scenario theoretically by developing a tight-binding Bogoliubov-de Gennes description starting from the Shiba bound states induced by the individual magnetic impurities. While the resulting model Hamiltonian has similarities with the Kitaev model for one-dimensional spinless p-wave superconductors, there are also important differences, most notably the long-range nature of hopping and pairing as well as the complex hopping amplitudes. We use both analytical and numerical approaches to explore the consequences of these differences for the phase diagram and the localization properties of the Majorana end states when the Shiba chain is in a topological superconducting phase.