2015/12/31 by Augusto L. Araújo, A. L. Araújo, Ernesto O. Wrasse +4
Materials Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Condensed matter physics #Dirac (video compression format) #Geometry #Graphene research and applications #Materials science #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Ribbon #Symmetry (geometry) #Symmetry protected topological order #Theoretical physics #Topological Materials and Phenomena #Topological insulator #Topological order #Topology (electrical circuits) #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.93.161101
published as Phys. Rev. B 93, 161101 (2016) · 9 pages, 4 figures
openalex publication_date 2016/04/04 · arxiv created 2016/04/12 · arxiv updated 2016/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
States of matter with nontrivial topology have been classified by their bulk symmetry properties. However, by cutting the topological insulator into ribbons, the symmetry of the system is reduced. By constructing effective Hamiltonians containing the proper symmetry of the ribbon, we find that the nature of topological states is dependent on the reduced symmetry of the ribbon and the appropriate boundary conditions. We apply our model to the recently discovered two-dimensional topological crystalline insulators composed by IV-VI monolayers, where we verify that the edge terminations play a major role on the Dirac crossings. Particularly, we find that some bulk cuts lead to nonsymmorphic ribbons, even though the bulk material is symmorphic. The nonsymmorphism yields a new topological protection, where the Dirac cone is preserved for arbitrary ribbon width. The effective Hamiltonians are in good agreement with ab initio calculations.