The \(\mathbb{Z}_{2}\) Invariant of Two-Dimensional Topological Insulators

  • János K. Asbóth
  • László Oroszlány
  • András Pályi
Part of the Lecture Notes in Physics book series (LNP, volume 919)


A time-reversal invariant topological insulator either has no topologically protected edge states, or one pair of such edge states. Thus, its bulk topological invariant is either 0 or 1: it is a \(\mathbb{Z}_{2}\) number. Although obtaining a single yes/no answer might seem easier than the calculation of a Chern number, the \(\mathbb{Z}_{2}\) invariant is notoriously difficult to calculate. In this chapter we detail a way to calculate it that follows the same logic as before for the Chern number.


Wilson Loop Edge State Topological Insulator Charge Pump Berry Phase 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • János K. Asbóth
    • 1
  • László Oroszlány
    • 2
  • András Pályi
    • 3
    • 4
  1. 1.Wigner Research Centre for PhysicsHungarian Academy of SciencesBudapestHungary
  2. 2.Department of Physics of Complex SystemsEötvös Loránd UniversityBudapestHungary
  3. 3.Department of Materials PhysicsEötvös Loránd UniversityBudapestHungary
  4. 4.Department of PhysicsBudapest University of Technology and EconomicsBudapestHungary

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