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Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter

  • Abhijeet Alase
Book
  • 1.1k Downloads

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Abhijeet Alase
    Pages 1-12
  3. Abhijeet Alase
    Pages 191-198
  4. Back Matter
    Pages 199-200

About this book

Introduction

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.

Keywords

Bloch's theorem Bulk-boundary correspondence Altland-Zirnbauer symmetry class topological boundary states gapless quasiparticle excitation stability of zero modes bulk fermionic wavefunction

Authors and affiliations

  • Abhijeet Alase
    • 1
  1. 1.Institute for Quantum Science and TechnologyUniversity of CalgaryCalgaryCanada

Bibliographic information