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Topologically Protected States in One-Dimensional Systems
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eBook
Topologically Protected States in One-Dimensional Systems
2017
Overview
We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or
“Dirac points”. We 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. Our 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 we construct can be
realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
Publisher
American Mathematical Society
Subject
ISBN
1470423235, 9781470423230
