Topologically Protected States in One-dimensional Systems

Ebook Details

Authors

C. F. Fefferman, J. P Lee-thorp, M. I. Weinstein

Year 2017
Pages 118
Publisher Amer Mathematical Society
Language en
ISBN 9781470423230
File Size 1.39 MB
File Format PDF
Download Counter 129
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Ebook Description

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.