Topologically Protected States in One-Dimensional Systems
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.
Cite
@article{arxiv.1405.4569,
title = {Topologically Protected States in One-Dimensional Systems},
author = {Charles L. Fefferman and James P. Lee-Thorp and Michael I. Weinstein},
journal= {arXiv preprint arXiv:1405.4569},
year = {2015}
}
Comments
To appear in Memoirs of the American Mathematical Society -- 100+ pages, 10 figures