The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They 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. The authors' 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 the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
ISBN: | 9781470423230 |
Publication date: | 30th May 2017 |
Author: | Charles Fefferman, J P LeeThorp, Michael I Weinstein |
Publisher: | American Mathematical Society |
Format: | Paperback |
Pagination: | 118 pages |
Series: | Memoirs of the American Mathematical Society |
Genres: |
Calculus and mathematical analysis Mathematical physics |