04424nam 22006615 450 991037393450332120200705233006.03-030-31960-110.1007/978-3-030-31960-1(CKB)4100000009844740(DE-He213)978-3-030-31960-1(MiAaPQ)EBC5982896(PPN)269146806(EXLCZ)99410000000984474020191120d2019 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierBoundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter[electronic resource] /by Abhijeet Alase1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (XVII, 200 p. 23 illus., 19 illus. in color.) Springer Theses, Recognizing Outstanding Ph.D. Research,2190-50533-030-31959-8 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.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.Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5053Solid state physicsPhase transitions (Statistical physics)Mathematical physicsPhysicsSemiconductorsSolid State Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P25013Phase Transitions and Multiphase Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P25099Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Semiconductorshttps://scigraph.springernature.com/ontologies/product-market-codes/P25150Solid state physics.Phase transitions (Statistical physics).Mathematical physics.Physics.Semiconductors.Solid State Physics.Phase Transitions and Multiphase Systems.Mathematical Physics.Mathematical Methods in Physics.Semiconductors.530.41Alase Abhijeetauthttp://id.loc.gov/vocabulary/relators/aut1064356MiAaPQMiAaPQMiAaPQBOOK9910373934503321Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter2537596UNINA