  We consider one-dimensional topological insulators hosting fractionally
charged midgap states in the presence and absence of induced superconductivity
pairing. Under the protection of a discrete symmetry, relating positive and
negative energy states, the solitonic midgap states remain pinned at zero
energy when superconducting correlations are induced by proximity effect. When
the superconducting pairing dominates the initial insulating gap, Majorana
fermion phases develop for a class of insulators. As a concrete example, we
study the Creutz model with induced s-wave superconductivity and repulsive
Hubbard-type interactions. For a finite wire, without interactions, the
solitonic modes originating from the nonsuperconducting model survive at zero
energy, revealing a fourfold-degenerate ground state. However, interactions
break the aforementioned discrete symmetry and completely remove this
degeneracy, thereby producing a unique ground state which ischaracterized by a
topological bulk invariant with respect to the product of fermion parity and
bond inversion. In contrast, the Majorana edge modes are globally robust to
interactions. Moreover, the parameter range for which a topological Majorana
phase is stabilized expands when increasing the repulsive Hubbard interaction.
The topological phase diagram of the interacting model is obtained using a
combination of mean-field theory and density matrix renormalization group
techniques.
