2006/04/30 by Rahul Roy · 12 citations
Materials Science · Mathematics · Physics and Astronomy · #Algorithm #Graphene research and applications #Homotopy #Invariant (physics) #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Topological Materials and Phenomena #Topological quantum computer #Wave function #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.79.195321
published as Phys. Rev. B 79, 195321 (2009) [4 pages] · Presentation changed to improve clarity, some technical aspects of the topological arguments including material previously cited as unpublished notes have now been added as an appendix
arxiv created 2006/09/18 · openalex publication_date 2009/05/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the phases of Bloch insulators with time-reversal symmetry on the basis of the homotopy of the ground-state wave functions in momentum space and find that there are two topological classes characterized by a Z2 invariant. The results are in agreement with a recent study based on counting the zeroes of a certain Pfaffian function related to the ground-state wave function. It is shown that there is a link between the formulation of the topological invariant presented here and the number of robust edge states. A formula is also provided which greatly simplifies the computation of the invariant in a large number of cases. The present study provides guidance for the search of systems which belong to the nontrivial topological class and also establishes a link between the quantum spin Hall effect and the integer quantum Hall effect.