Topologically Protected States in OneDimensional Systems
Abstract
We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear bandcrossings 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 zeroenergy mode of an asymptotic onedimensional Dirac operator. Our model captures many aspects of the phenomenon of topologically protected edge states for twodimensional 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 phasedefect.
 Publication:

arXiv eprints
 Pub Date:
 May 2014
 DOI:
 10.48550/arXiv.1405.4569
 arXiv:
 arXiv:1405.4569
 Bibcode:
 2014arXiv1405.4569F
 Keywords:

 Mathematical Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematics  Analysis of PDEs;
 Quantum Physics
 EPrint:
 To appear in Memoirs of the American Mathematical Society  100+ pages, 10 figures