Z2 anomaly and boundaries of topological insulators

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We study the edge and surface theories of topological insulators from the perspective of anomalies and identify a Z2 anomaly associated with charge conservation. The anomaly is manifested through a two-point correlation function involving creation and annihilation operators on two decoupled boundaries. Although charge conservation on each boundary requires this quantity to vanish, we find that it diverges. A corollary result is that under an insertion of a flux quantum, the ground state evolves to an exactly orthogonal state independent of the rate at which the flux is inserted. The anomaly persists in the presence of disorder and imposes sharp restrictions on possible low-energy theories. Being formulated in a many-body, field-theoretical language, the anomaly allows one to test the robustness of topological insulators to interactions in a concise way.

Original languageEnglish
Article number115307
Number of pages8
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
StatePublished - 17 Sep 2013

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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