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.