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Topologically Protected States in One-Dimensional Systems

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Topologically Protected States in One-Dimensional Systems Synopsis

The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They then show that the introduction of an ``edge'', via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized ``edge states''. These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.

About This Edition

ISBN: 9781470423230
Publication date:
Author: Charles Fefferman, J P LeeThorp, Michael I Weinstein
Publisher: American Mathematical Society
Format: Paperback
Pagination: 118 pages
Series: Memoirs of the American Mathematical Society
Genres: Calculus and mathematical analysis
Mathematical physics