Boundary effects in two-band superconductors

We present a microscopic study of the behavior of the order parameters near the boundaries of a two-band superconducting material, described by the standard tight-binding Bardeen-Cooper-Schrieffer model. We find superconducting surface states. The relative difference between bulk and surface critical temperatures is a nontrivial function of the interband coupling strength. For superconductors with weak interband coupling, boundaries induce variations of the gaps with the presence of multiple length scales, despite nonzero interband Josephson coupling.