Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter [[electronic resource] /] / by Abhijeet Alase

• Autore: Alase Abhijeet
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019
• Edizione: 1st ed. 2019.
• Descrizione fisica: 1 online resource (XVII, 200 p. 23 illus., 19 illus. in color.)
• Disciplina: 530.41
• Soggetto topico: 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
• Nota di contenuto: 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.
• Sommario/riassunto: 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 dimension.
• Titolo autorizzato: Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter
• ISBN: 3-030-31960-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910373934503321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Theses, Recognizing Outstanding Ph.D. Research, . 2190-5053