Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter / by Abhijeet Alase.

Format:

Book

Author/Creator:

Alase, Abhijeet, author.

Contributor:

SpringerLink (Online service)

Series:

Physics and Astronomy (Springer-11651)

Springer Theses, Recognizing Outstanding Ph.D. Research,. 2190-5053

Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5053

Language:

English

Subjects (All):

Solid state physics.

Phase transformations (Statistical physics).

Mathematical physics.

Physics.

Semiconductors.

Solid State Physics.

Phase Transitions and Multiphase Systems.

Mathematical Physics.

Mathematical Methods in Physics.

Local Subjects:

Solid State Physics.

Phase Transitions and Multiphase Systems.

Mathematical Physics.

Mathematical Methods in Physics.

Semiconductors.

Physical Description:

1 online resource (XVII, 200 pages) : 23 illustrations, 19 illustrations in color.

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

978-3-030-31960-1

9783030319601

Access Restriction:

Restricted for use by site license.