Effect of hybridization symmetry on topological phases of odd-parity multiband superconductors

We study two-band one-dimensional superconducting chains of spinless fermions with inter and intra-band pairing. These bands hybridize and depending on the relative angular momentum of their orbitals this can be symmetric or anti-symmetric. The competition between intra and inter-band superconductivity and how it is affected by the symmetry of the hybridization is investigated. The interband pairing is shown to be dominant on a large region of parameter space. A rich phase diagram is found in the presence of anti-symmetric hybridization. The topological properties of the model are obtained through the topological invariant winding number. We find the existence of a topological phase due to the inter-band superconductivity and induced by symmetric hybridization. Robustness of zero-energy edge states are discussed and are shown to be present in the topological phase.