Topologically protected states in one-dimensional continuous systems and Dirac points.
basic_science · Level V
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- Record sourced from PubMed, PMID 24927571.
- Also identified by DOI 10.1073/pnas.1407391111 and PMC identifier 4066501.
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Abstract
We study a class of periodic Schrödinger operators on ℝ that have Dirac points. The introduction of an "edge" 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 transverse-magnetic electromagnetic modes for a class of photonic waveguides with a phase defect. Our model captures many aspects of the phenomenon of topologically protected edge states for 2D bulk structures such as the honeycomb structure of graphene.