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Boundary physics and bulk-boundary c...

Alase, Abhijeet.

Boundary physics and bulk-boundary correspondence in topological phases of matter

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Boundary physics and bulk-boundary correspondence in topological phases of matterby Abhijeet Alase.
作者:	Alase, Abhijeet.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	xvii, 200 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Boundary element methods.
電子資源:	https://doi.org/10.1007/978-3-030-31960-1
ISBN:	9783030319601$q(electronic bk.)

Boundary physics and bulk-boundary correspondence in topological phases of matter
Alase, Abhijeet.

Boundary physics and bulk-boundary correspondence in topological phases of matter[electronic resource] /by Abhijeet Alase. - Cham :Springer International Publishing :2019. - xvii, 200 p. :ill., digital ;24 cm. - Springer theses,2190-5053. - Springer theses..

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.

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.

ISBN: 9783030319601$q(electronic bk.)

Standard No.: 10.1007/978-3-030-31960-1doiSubjects--Topical Terms:

208685
Boundary element methods.

LC Class. No.: TA347.B69 / A53 2019

Dewey Class. No.: 530.41

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520 $a 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.
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