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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 |
|---|---|
| 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 |
Tabla de Contenidos:
- Chapter 1. Introduction and Outline Chapter 2. Floquet-Bloch and Fourier Analysis Chapter 3. Dirac Points of 1D Periodic Structures Chapter 4. Domain Wall Modulated Periodic Hamiltonian and Formal Derivation of Topologically Protected Bound States Chapter 5. Main Theorem
- Bifurcation of Topologically Protected States Chapter 6. Proof of the Main Theorem Appendix A. A Variant of Poisson Summation Appendix B. 1D Dirac points and Floquet-Bloch Eigenfunctions Appendix C. Dirac Points for Small Amplitude Potentials Appendix D. Genericity of Dirac Points
- 1D and 2D cases Appendix E. Degeneracy Lifting at Quasi-momentum Zero Appendix F. Gap Opening Due to Breaking of Inversion Symmetry Appendix G. Bounds on Leading Order Terms in Multiple Scale Expansion Appendix H. Derivation of Key Bounds and Limiting Relations in the Lyapunov-Schmidt Reduction.