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We revisit the problem of Majorana states in chains of scalar impuritiesdeposited on a superconductor with a mixed s-wave and p-wave pairing. We alsostudy the formation of Majorana states for magnetic impurity chains. We findthat the magnetic impurity chains exhibit well-localized Majorana states whenthe substrate is trivial, but these states hybridize and get dissolved in thebulk when the substrate is topological. Most surprisingly, and contrary toprevious predictions, the scalar impurity chain does not support fullylocalized Majorana states except for very small and finely tuned parameterregimes, mostly for a non-topological substrate close to the topologicaltransition. Our results indicate that a purely p-wave or a dominant p-wavesubstrate are not good candidates to support either magnetic or scalar impuritytopological Shiba chains.

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