We present a simple two-dimensional hopping model for independent electrons which has strictly localized states in addition to the extended states. These localized states can exist either in a band gap or within the continuum. The localized states persist if the lattice periodicity is destroyed. Finally, the effect is shown to hold for a much more general class of systems.

• Received 20 January 1986

DOI:https://doi.org/10.1103/PhysRevB.34.5208