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Topologically protected states in one-dimensional systems /
We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "mDirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in th...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2017.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1173. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "mDirac 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 zero-energy mode of an asymptotic one-dimensional Dirac operator. Our 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 we construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect. |
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| Notas: | "Volume 247, number 1173 (sixth of 7 numbers), May 2017." Schrödinger equation, Dirac equation, Floquet-Bloch theory, topological protection, edge states, Hill's equation, domain wall. |
| Descripción Física: | 1 online resource (vii, 118 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 117-118). |
| ISBN: | 9781470437077 1470437074 |
| ISSN: | 0065-9266 ; |