Alase Abhijeet Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter 9783030319595

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Автор: Alase Abhijeet
Название: Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter
ISBN: 9783030319595
Издательство: Springer
Классификация:

Физика конденсированных сред (физика веществ в жидком и твёрдом состоянии)

Математическая физика

Полупроводники и сверхпроводники

ISBN-10: 3030319598
Обложка/Формат: Hardcover
Страницы: 200
Вес: 0.49 кг.
Дата издания: 09.01.2020
Серия: Springer theses
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 22 tables, color; 19 illustrations, color; 4 illustrations, black and white; xvii, 200 p. 23 illus., 19 illus. in color.
Размер: 234 x 156 x 14
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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 Blochs Theorem. A cornerstone of electronic band structure and transport theory in crystalline matter, Blochs 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.
Дополнительное описание: 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.

Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter, Alase Abhijeet