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Bulk-Edge Correspondence for Two-Dimensional Topological Insulators

Communications in Mathematical Physics volume 324, pages 851–895 (2013)Cite this article

Abstract

Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle picture. We give a new formulation of the \({\mathbb{Z}_{2}}\)-invariant, which allows for a bulk index not relying on a (two-dimensional) Brillouin zone. When available though, that index is shown to agree with known formulations. The method also applies to integer quantum Hall systems. We discuss a further variant of the correspondence, based on scattering theory.

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Authors and Affiliations

  1. Theoretische Physik, ETH Zurich, 8093, Zurich, Switzerland

    Gian Michele Graf & Marcello Porta

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  1. Gian Michele Graf
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  2. Marcello Porta
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Correspondence to Marcello Porta.

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Communicated by M. Aizenman

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Graf, G.M., Porta, M. Bulk-Edge Correspondence for Two-Dimensional Topological Insulators. Commun. Math. Phys. 324, 851–895 (2013). https://doi.org/10.1007/s00220-013-1819-6

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  • DOI: https://doi.org/10.1007/s00220-013-1819-6

Keywords

  • Vector Bundle
  • Edge State
  • Topological Insulator
  • Quantum Hall Effect
  • Fermi Line