Topologically Protected States in One-Dimensional Systems (Memoirs of the American Mathematical Society) - Softcover

Fefferman, C.F.; Lee-Thorp, J.P.; Weinstein, M.I.

Softcover

ISBN 10: 1470423235 ISBN 13: 9781470423230

Publisher: American Mathematical Society, 2017

Synopsis

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.

About this title

About the Author

C. F. Fefferman, Princeton University, New Jersey.

J. P. Lee-Thorp, Columbia University, New York, NY.

M. I. Weinstein, Columbia University, New York, NY.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2017
• Language: English
• ISBN 10: 1470423235
• ISBN 13: 9781470423230
• Binding: Paperback
• Number of pages: 118