%0 Journal Article
%T Topologically Protected States in One-Dimensional Systems
%A Charles L. Fefferman
%A James P. Lee-Thorp
%A Michael I. Weinstein
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1405.4569v2