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Record Nr. |
UNINA9910373934503321 |
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Autore |
Alase Abhijeet |
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Titolo |
Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter [[electronic resource] /] / by Abhijeet Alase |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
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ISBN |
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Edizione |
[1st ed. 2019.] |
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Descrizione fisica |
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1 online resource (XVII, 200 p. 23 illus., 19 illus. in color.) |
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Collana |
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Springer Theses, Recognizing Outstanding Ph.D. Research, , 2190-5053 |
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Disciplina |
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Soggetti |
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Solid state physics |
Phase transitions (Statistical physics) |
Mathematical physics |
Physics |
Semiconductors |
Solid State Physics |
Phase Transitions and Multiphase Systems |
Mathematical Physics |
Mathematical Methods in Physics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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 Outlook. |
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Sommario/riassunto |
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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 |
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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 dimension. |
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