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Matrix Factorization Approach to Bulk-Boundary Correspondence

  • Abhijeet Alase
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

We introduce a new approach based on matrix factorization to obtain a unified proof of the bulk-boundary correspondence for the five Altland–Zirnbauer symmetry classes, to which one-dimensional non-trivial topological systems belong. A rigorous definition of “stability” of zero modes is provided with the aim of bringing clarity to various claims in the literature about topological “protection” of boundary-localized states. We also explore how the topology of the bulk fermionic wavefunctions and the symmetries of a system influence the stability of the zero-energy modes.

Keywords

Topological insulators Topological superconductors Symmetry-protected topological phases Bulk-boundary correspondence Wiener–Hopf factorization Topological protection 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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