  There is no assurance that interface states can be found at the boundary
separating two materials. As a strong perturbation typically favors wave
localization, it is natural to expect that an interface state should form more
easily in the boundary that represents a strong perturbation. Here, we show on
the contrary that in some two dimensional photonic crystals (PCs) with a square
lattice possessing Dirac-like cone at k=0, a small perturbation guarantees the
existence of interface states. More specifically, we find that single-mode
localized states exist in a deterministic manner at an interface formed by two
PCs each with system parameters slightly perturbed from the conical dispersion
condition. The conical dispersion guarantees the existence of gaps in the
projected band structure which allows interface states to form and the assured
existence of interface states stems from the geometric phases of the bulk
bands.
