  We consider a one-dimensional system combining local magnetic moments and a
delocalized metallic band on top of a superconducting substrate. This system
can describe a chain of magnetic impurities with both localized polarized
orbitals and delocalized s-like orbitals or a conducting wire with embedded
magnetic impurities. We study the interplay between the one-dimensional Shiba
band physics arising from the interplay between magnetic moments and the
substrate and the delocalized wire-like conduction band on top of the
superconductor. We derive an effective low-energy Hamiltonian in terms of two
coupled asymmetric Kitaev-like Hamiltonians and analyze its topological
properties. We have found that this system can host multiple Majorana bound
states at its extremities provided a magnetic mirror symmetry is present. We
compute the phase diagram of the system depending on the magnetic exchange
interactions, the impurity distance and especially the coupling between both
bands. In presence of inhomogeneities which typically break this magnetic
mirror symmetry, we show that the coexistence of a Shiba and wire delocalized
topological band can drive the system into a non-topological regime with a
splitting of Majorana bound states.
