|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Edge states in honeycomb structures | | Charles L. Fefferman
; James P. Lee-Thorp
; Michael I. Weinstein
; | | Date: |
19 Jun 2015 | | Abstract: | An edge state is a time-harmonic solution of a conservative wave system, e.g.
Schr"odinger, Maxwell, which is propagating (plane-wave-like) parallel to, and
localized transverse to, a line-defect or "edge." Topologically protected edge
states are edge states which are stable against spatially localized (even
strong) deformations of the edge. First studied in the context of the quantum
Hall effect, protected edge states have attracted huge interest due to their
role in the field of topological insulators. Theoretical understanding of
topological protection has mainly come from discrete (tight-binding) models and
direct numerical simulation. In this paper we consider a rich family of
continuum PDE models for which we rigorously study regimes where topologically
protected edge states exist.
Our model is a class of Schroedinger operators on R^2 with a background
two-dimensional honeycomb potential perturbed by an "edge-potential." The edge
potential is a domain-wall interpolation, transverse to a prescribed "rational"
edge, between two distinct periodic structures. General conditions are given
for the bifurcation of a branch of topologically protected edge states from
Dirac points of the background honeycomb structure. The bifurcation is seeded
by the zero mode of a one-dimensional effective Dirac operator. A key condition
is a spectral no-fold condition for the prescribed edge.
We then use this result to prove the existence of topologically protected
edge states along zigzag edges of certain honeycomb structures. Our results are
consistent with the physics literature and appear to be the first rigorous
results on the existence of topologically protected edge states for continuum
2D PDE systems. We also show that the family of Hamiltonians we study contains
cases where zigzag edge states exist, but which are not topologically
protected. | | Source: | arXiv, 1506.6111 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER