Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter (Springer Theses) - Image 1

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Springer Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter (Springer Theses)

Name: Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter (Springer Theses)
Brand: Springer
Price: 103.81 GBP
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Electronics Engineering

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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. From the Back Cover 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. About the Author 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.

Product Specifications

Brand: Springer
Format: hardcover
ASIN: 3030319598
Category: Books > Subjects > Science, Nature & Maths > Engineering & Technology > Electronics & Communications Engineering > Electronics Engineering
Domain: Amazon UK
Release Date: 06 December 2019
Listed Since: 24 August 2019

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Springer Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter (Springer Theses)

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