Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter (Hardcover, 1st ed. 2019)

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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Springer Theses
Release date:	December 2019
First published:	2019
Authors:	Abhijeet Alase
Dimensions:	235 x 155mm (L x W)
Format:	Hardcover
Pages:	200
Edition:	1st ed. 2019
ISBN-13:	978-3-03-031959-5
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > General Books > Science & Mathematics > Physics > States of matter > Condensed matter physics (liquids & solids) Books > Professional & Technical > Electronics & communications engineering > Electronics engineering > Electronic devices & materials > Semi-conductors & super-conductors Books > Science & Mathematics > Chemistry > Analytical chemistry > Qualitative analytical chemistry > Chemical spectroscopy, spectrochemistry > General
LSN:	3-03-031959-8
Barcode:	9783030319595

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