Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter / Abhijeet Alase

By:

Alase, Abhijeet [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Theses Recognizing Outstanding Ph.D. Research | Springer Theses, Recognizing Outstanding Ph.D. Research | Springer eBooks Physics and Astronomy | Springer eBook CollectionPublisher: Cham : Springer, [2019]Copyright date: © 2019Description: 1 Online-Ressource (XVII, 200 Seiten) : Illustrationen, DiagrammeISBN:

9783030319601

Subject(s): Genre/Form:

Hochschulschrift

Additional physical formats: 9783030319595 | Erscheint auch als: 978-3-030-31959-5 Druck-AusgabeLOC classification:

QC176-176.9

DOI: DOI: 10.1007/978-3-030-31960-1Online resources:

Dissertation note: Dissertation - Dartmouth University Summary: Chapter1: Introduction -- Chapter2: Generalization of Bloch's theorem to systems with boundary -- Chapter3: Investigation of topological boundary states via generalized Bloch theorem -- Chapter4: Matrix factorization approach to bulk-boundary correspondence -- Chapter5: Mathematical foundations to the generalized Bloch theorem -- Chapter6: Summary and OutlookSummary: This thesis extends our understanding of systems of independent electrons by developing a generalization of Bloch’s Theorem which is applicable whenever translational symmetry is broken solely due to arbitrary boundary conditions. The thesis begins with a historical overview of topological condensed matter physics, placing the work in context, before introducing the generalized form of Bloch's Theorem. A cornerstone of electronic band structure and transport theory in crystalline matter, Bloch's Theorem is generalized via a reformulation of the diagonalization problem in terms of corner-modified block-Toeplitz matrices and, physically, by allowing the crystal momentum to take complex values. This formulation provides exact expressions for all the energy eigenvalues and eigenstates of the single-particle Hamiltonian. By precisely capturing the interplay between bulk and boundary properties, this affords an exact analysis of several prototypical models relevant to symmetry-protected topological phases of matter, including a characterization of zero-energy localized boundary excitations in both topological insulators and superconductors. Notably, in combination with suitable matrix factorization techniques, the generalized Bloch Hamiltonian is also shown to provide a natural starting point for a unified derivation of bulk-boundary correspondence for all symmetry classes in one dimensionPPN: PPN: 1684970342Package identifier: Produktsigel: ZDB-2-PHA | ZDB-2-SEB | ZDB-2-SXP

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