Topological Nonsymmorphic Ribbons out of Symmorphic Bulk

Abstract

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.

arXiv comment9 pages, 4 figures

References in corpus (25)

• Topological Insulators
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Crystalline Insulators
• Topological Crystalline Insulators in the SnTe Material Class
• Electronic States of Graphene Nanoribbons
• Experimental realization of a topological crystalline insulator in SnTe
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Dirac Semimetals in Two Dimensions
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• The space group classification of topological band insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Observation of Dirac node formation and mass acquisition in a topological crystalline insulator
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topological non-symmorphic crystalline insulators
• Topological Classification of Crystalline Insulators with Point Group Symmetry
• Crystal Field Effect Induced Topological Crystalline Insulators In Monolayer IV-VI Semiconductors
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Finite-size-effect-induced topological phase transition in a topological crystalline insulator
• Topological Crystalline Insulator and Quantum Anomalous Hall States in IV-VI based Monolayers and their Quantum Wells

Cited by in corpus (5)

• Discovery of a two-dimensional topological insulator in SiTe
• Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family
• Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians
• Competing edge structures of Sb and Bi bilayers by trivial and nontrivial band topologies
• Non-Trivial Topological Phase in the Sn_{1-x}In_xTe Superconductor