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Titlebook: Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter; Abhijeet Alase Book 2019 Springer Nature Switzerland AG

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發(fā)表于 2025-3-21 18:22:33 | 只看該作者 |倒序瀏覽 |閱讀模式
期刊全稱Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter
影響因子2023Abhijeet Alase
視頻videohttp://file.papertrans.cn/191/190024/190024.mp4
發(fā)行地址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 appli
學(xué)科分類Springer Theses
圖書封面Titlebook: Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter;  Abhijeet Alase Book 2019 Springer Nature Switzerland AG
影響因子.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 f
Pindex Book 2019
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沙發(fā)
發(fā)表于 2025-3-21 23:51:04 | 只看該作者
Low-Dimensional Structures in SemiconductorsWe analyze several 1D and 2D topological lattice Hamiltonians using the generalization of Bloch’s theorem developed in Chap. .. Apart from providing exact solutions for several important models, the analyses of various models in this chapter also serve as illustrations for using the framework of generalized Bloch theorem.
板凳
發(fā)表于 2025-3-22 04:01:24 | 只看該作者
地板
發(fā)表于 2025-3-22 06:22:23 | 只看該作者
Introduction,This chapter provides a non-technical overview of the field of topological insulators and superconductors. The current status and challenges in the theoretical investigations are discussed, which serve as the motivation for the work presented in the remainder of the chapters. A brief outline of all chapters is provided at the end.
5#
發(fā)表于 2025-3-22 09:59:47 | 只看該作者
Investigation of Topological Boundary States via Generalized Bloch Theorem,We analyze several 1D and 2D topological lattice Hamiltonians using the generalization of Bloch’s theorem developed in Chap. .. Apart from providing exact solutions for several important models, the analyses of various models in this chapter also serve as illustrations for using the framework of generalized Bloch theorem.
6#
發(fā)表于 2025-3-22 15:23:18 | 只看該作者
Summary and Outlook,The key findings of the previous chapters are summarized, along with possible directions of future research.
7#
發(fā)表于 2025-3-22 20:49:52 | 只看該作者
J. S. Rimmer,B. Hamilton,A. R. Peakerroken solely due to .. This generalization, which is made possible mainly by allowing the crystal momentum to take complex values, provides exact analytic expressions for . energy eigenvalues and eigenvectors of the system Hamiltonian. A remarkable consequence of this theorem is the predicted emerge
8#
發(fā)表于 2025-3-22 22:36:03 | 只看該作者
Low-Dimensional Structures in Semiconductors symmetry classes, to which one-dimensional non-trivial topological systems belong. A rigorous definition of “stability” of zero modes is provided with the aim of bringing clarity to various claims in the literature about topological “protection” of boundary-localized states. We also explore how the
9#
發(fā)表于 2025-3-23 04:28:09 | 只看該作者
Low-Dimensional Structures in Semiconductors non-Hermitian block-Toeplitz matrices, so as to keep the formalism as general as possible. There are two main takeaways as part of the proof of the generalized Bloch theorem: First, a simple yet effective separation of the time-independent Schr?dinger equation into bulk and boundary equations is wh
10#
發(fā)表于 2025-3-23 05:51:29 | 只看該作者
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