We investigate the effects of non-magnetic disorder in a hybridized two-dimensional two-orbital s-wave superconductor (SC) model. The situation in which electronic orbitals overlap such that the hybridizationVi,jamong them is antisymmetric, under inversion symmetry, was taken into account. The on-site disorder is given by a random impurity potential. We find that while the random disorder acts to the detriment of superconductivity, hybridization proceeds to favor it. Accordingly, hybridization plays an important role in two-orbital models of superconductivity, in order to hold the long-range order against the increase of disorder. This makes the present model eligible to describe real materials, since the hybridization may be induced by pressure or doping. In addition, the regime from moderate to strong disorder reveals that the system is broken into SC islands with correlated local order parameters. These correlations persist to distances of several order lattice spacing which corresponds to the size of the SC-Islands.
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