In this paper we study the effects of hybridization in the superconducting properties of a two-band system. We consider the cases that these bands are formed by electronic orbitals with angular momentum, such that, the hybridization $V(mathbf{k})$ among them can be symmetric or antisymmetric under inversion symmetry. We take into account only intra-band attractive interactions in the two bands and investigate the appearance of an induced inter-band pairing gap. We show that (inter-band) superconducting orderings are induced in the total absence of attractive interaction between the two bands, which turns out to be completely dependent on the hybridization between them. For the case of antisymmetric hybridization we show that the induced inter-band superconductivity has a p-wave symmetry.
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