We consider the existence of localized modes corresponding to eigenvalues of
the periodic Schr\"{o}dinger operator $-\partial_x^2+ V(x)$ with an interface.
The interface is modeled by a jump either in the value or the derivative of
$V(x)$ and, in general, does not correspond to a localized perturbation of the
perfectly periodic operator. The periodic potentials on each side of the
interface can, moreover, be different. As we show, eigenvalues can only occur
in spectral gaps.