LEADER 04404nam 22006615 450 001 9910373934503321 005 20200705233006.0 010 $a3-030-31960-1 024 7 $a10.1007/978-3-030-31960-1 035 $a(CKB)4100000009844740 035 $a(DE-He213)978-3-030-31960-1 035 $a(MiAaPQ)EBC5982896 035 $a(PPN)269146806 035 $a(EXLCZ)994100000009844740 100 $a20191120d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBoundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter /$fby Abhijeet Alase 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XVII, 200 p. 23 illus., 19 illus. in color.) 225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053 311 $a3-030-31959-8 327 $aChapter1: 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. 330 $aThis thesis extends our understanding of systems of independent electrons by developing a generalization of Bloch?s Theorem which is applicable whenever translational symmetry is broken solely due to arbitrary boundary conditions. The thesis begins with a historical overview of topological condensed matter physics, placing the work in context, before introducing the generalized form of Bloch's Theorem. A cornerstone of electronic band structure and transport theory in crystalline matter, Bloch's Theorem is generalized via a reformulation of the diagonalization problem in terms of corner-modified block-Toeplitz matrices and, physically, by allowing the crystal momentum to take complex values. This formulation provides exact expressions for all the energy eigenvalues and eigenstates of the single-particle Hamiltonian. By precisely capturing the interplay between bulk and boundary properties, this affords an exact analysis of several prototypical models relevant to symmetry-protected topological phases of matter, including a characterization of zero-energy localized boundary excitations in both topological insulators and superconductors. Notably, in combination with suitable matrix factorization techniques, the generalized Bloch Hamiltonian is also shown to provide a natural starting point for a unified derivation of bulk-boundary correspondence for all symmetry classes in one dimension. 410 0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053 606 $aSolid state physics 606 $aPhase transformations (Statistical physics) 606 $aMathematical physics 606 $aPhysics 606 $aSemiconductors 606 $aSolid State Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25013 606 $aPhase Transitions and Multiphase Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P25099 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aSemiconductors$3https://scigraph.springernature.com/ontologies/product-market-codes/P25150 615 0$aSolid state physics. 615 0$aPhase transformations (Statistical physics) 615 0$aMathematical physics. 615 0$aPhysics. 615 0$aSemiconductors. 615 14$aSolid State Physics. 615 24$aPhase Transitions and Multiphase Systems. 615 24$aMathematical Physics. 615 24$aMathematical Methods in Physics. 615 24$aSemiconductors. 676 $a530.41 700 $aAlase$b Abhijeet$4aut$4http://id.loc.gov/vocabulary/relators/aut$01064356 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910373934503321 996 $aBoundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter$92537596 997 $aUNINA