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Topologically protected states in one-dimensional systems

Author: Charles Fefferman; J P Lee-Thorp; Michael I Weinstein; American Mathematical Society,
Publisher: Providence, Rhode Island : American Mathematical Society, 2017. ©2017
Series: Memoirs of the American Mathematical Society, no. 1173.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Fefferman, Charles, 1949-
Topologically protected states in one-dimensional systems
(DLC) 2017010052
(OCoLC)972427493
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Charles Fefferman; J P Lee-Thorp; Michael I Weinstein; American Mathematical Society,
ISBN: 9781470437077 1470437074
OCLC Number: 982297192
Notes: "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
Description: 1 online resource (vii, 118 pages) : illustrations.
Contents: 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
Series Title: Memoirs of the American Mathematical Society, no. 1173.
Responsibility: C.L. Fefferman, J.P. Lee-Thorp, M.I. Weinstein.

Abstract:

Examines a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". The authors then show that the introduction of an  Read more...

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