  Chains of magnetic atoms placed on the surface of an s-wave superconductor
with large spin-orbit coupling provide a promising platform for the realization
of topological superconducting states characterized by the presence of Majorana
zero-energy modes. In this work we study the properties of the one-dimensional
chain of Yu-Shiba-Rusinov states induced by magnetic impurities using a
realistic model for the magnetic atoms that include the presence of multiple
scattering channels. These channels are mixed by the spin-orbit coupling and,
via the hybridization of the Yu-Shiba-Rusinov states at different sites of the
chain, result in a multi-band structure for the chain. We obtain the
topological phase diagram for such band structure. We identify the parameter
regimes for which the different bands lead to a topological phase and show that
the inclusion of higher bands can greatly enlarge the phase space for the
realization of topological states.
