By judiciously constructing local defects in graph models of multi-layer graphene, bound states can be constructed at energies that lie within the continuous spectrum of the associated Schrödinger operator. The layers may be stacked in AA or AB fashion. A necessary condition for this construction is the reducibility of the Fermi surface for the multi-layer structure. This is achieved due to a special reduction of the complex dispersion relation to a function of a single polynomial "composite" function of the quasimomenta.
This is joint work with Wei Li and Stephen Shipman at LSU.