Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter: Springer Theses
Autor Abhijeet Alaseen Limba Engleză Paperback – 26 dec 2020
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Paperback (1) | 921.82 lei 6-8 săpt. | |
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Hardback (1) | 927.68 lei 6-8 săpt. | |
Springer International Publishing – 6 dec 2019 | 927.68 lei 6-8 săpt. |
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Specificații
ISBN-13: 9783030319625
ISBN-10: 3030319628
Pagini: 200
Ilustrații: XVII, 200 p. 23 illus., 19 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.31 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Springer Theses
Locul publicării:Cham, Switzerland
ISBN-10: 3030319628
Pagini: 200
Ilustrații: XVII, 200 p. 23 illus., 19 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.31 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Springer Theses
Locul publicării:Cham, Switzerland
Cuprins
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.
Notă biografică
Abhijeet Alase is a postdoctoral researcher at the Institute for Quantum Science and Technology of the University of Calgary. He received his PhD from Dartmouth College in 2019.
Textul de pe ultima copertă
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.
Caracteristici
Nominated as an outstanding PhD thesis by Dartmouth College Deepens understanding of topological phases via the bulk-boundary correspondence Describes a generalization of Bloch's theorem and its application to several relevant models of topological phases