Instability of Majorana states in Shiba chains due to leakage into a topological substrate

TL;DR

This paper investigates the stability of Majorana states in impurity chains on superconductors, revealing that leakage into a topological substrate destabilizes these states and that scalar impurity chains rarely support localized Majoranas.

Contribution

It demonstrates that Majorana states in impurity chains are destabilized by topological substrates and challenges previous assumptions about scalar impurity chains supporting localized Majoranas.

Findings

Magnetic impurity chains have localized Majoranas on trivial substrates.

Majorana states hybridize and dissolve in topological substrates.

Scalar impurity chains rarely support fully localized Majoranas except under fine-tuned conditions.

Abstract

We revisit the problem of Majorana states in chains of scalar impurities deposited on a superconductor with a mixed s-wave and p-wave pairing. We also study the formation of Majorana states for magnetic impurity chains. We find that the magnetic impurity chains exhibit well-localized Majorana states when the substrate is trivial, but these states hybridize and get dissolved in the bulk when the substrate is topological. Most surprisingly, and contrary to previous predictions, the scalar impurity chain does not support fully localized Majorana states except for very small and finely tuned parameter regimes, mostly for a non-topological substrate close to the topological transition. Our results indicate that a purely p-wave or a dominant p-wave substrate are not good candidates to support either magnetic or scalar impurity topological Shiba chains.