Topologically Protected States In One Dimensional Systems
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Topologically Protected States in One-dimensional Systems
Author | : Charles Fefferman |
Publisher | : |
Total Pages | : 118 |
Release | : 2017 |
Genre | : Dirac equation |
ISBN | : 9781470437077 |
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We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "mDirac 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.
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