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arXiv · 1405.4569

Topologically Protected States in One-Dimensional Systems

Charles L. Fefferman·James P. Lee-Thorp·Michael I. Weinstein
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Abstract

We study a class of periodic Schr\"odinger 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.

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Charles L. Fefferman, James P. Lee-Thorp, Michael I. Weinstein. 2014-05-19. Topologically Protected States in One-Dimensional Systems. https://arxiv.org/abs/1405.4569

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