Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 111, Issue 24, Pages 8759-8763Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1407391111
Keywords
Floquet-Bloch theory; Hill's equation; surface states; multiple scale analysis; wave-packets
Categories
Funding
- National Science Foundation (NSF) [DMS-1265524, DMS-10-08855]
- Columbia University Optics and Quantum Electronics Integrative Graduate Education and Research Traineeship (IGERT) NSF Grant [DGE-1069420]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1008855] Funding Source: National Science Foundation
Ask authors/readers for more resources
We study a class of periodic Schrodinger operators on R that have Dirac points. The introduction of an edge via adiabatic modulation of a periodic potential by a domain wall results in the bifurcation of spatially localized edge states, associated with the topologically protected zero-energymode of an asymptotic one-dimensional Dirac operator. The bound states we construct can be realized as highly robust transverse-magnetic electromagnetic modes for a class of photonic waveguides with a phase defect. Our model captures many aspects of the phenomenon of topologically protected edge states for 2D bulk structures such as the honeycomb structure of graphene.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available