  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.
