Abstract
We study a class of periodic Schrodinger operators, which we prove have Dirac points. We then show that the introduction of an via adiabatic modulation of a periodic potential by a domain wall results in the bifurcation of spatially localized \edge states, associated with the topologically protected zero- energy mode of an asymptotic one-dimensional Dirac operator. The bound states we construct can be realized as highly robust TM- electromagnetic modes for a class of photonic waveguides with a phase-defect. Our model also captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene.
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