Communications in Mathematical Physics

, Volume 324, Issue 3, pp 851–895 | Cite as

Bulk-Edge Correspondence for Two-Dimensional Topological Insulators

  • Gian Michele Graf
  • Marcello PortaEmail author


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.


Vector Bundle Edge State Topological Insulator Quantum Hall Effect Fermi Line 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Theoretische PhysikETH ZurichZurichSwitzerland

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