Isolantes topológicos protegidos por simetria cristalina

Abstract

The main purpose of this work is to investigate structural, electronic and topological properties of a new class of materials called Topological Crystalline Insulators, present in the semiconductors of the IV-VI family (PbSe, PbTe and SnTe). We start by studying the bulk properties of two- and three-dimensional topological non-trivial systems. Then finite-sized nanostructures composed of nanoribbons and stacking of monolayers have been addressed. Nanostructured topological/trivial interfaces are of great interest for potential technological applications, as well the characterization of the interface protected topological states. PbSe monolayer has been used as our two-dimensional non-trivial model protected by crystal symmetry. We investigate the effects of distinct termination edges on the topological state properties. By cutting the monolayer in two distinct crystallographic directions, it provides us with five distinct tape configurations. We demonstrate that, although the topological classification of an insulator is a bulk property, the distinct termination edge symmetry dictates the properties of the topological states. Our results also reveal an additional topological protection, induced by nonsymmorphic symmetry, demanding a Dirac crossing for nanoribbons of narrow width. This protection could not be predicted by the topological classification of the bulk, since the bulk has symmorphic symmetry. Monolayer and three-dimensional bulk SnTe present non-trivial phases, protected by crystal symmetry. Our calculations show a non-monotonic evolution of the band gap, by stacking SnTe monolayers, that has been explained based on the symmetry stacking. We verify that odd stacking is symmorphic, while even stacking has nonsymmorphic symmetry. For few monolayers we demonstrate that the proper symmetry of the system dictates it topological order. Also the topological protected states are strongly affected by the proper slab symmetry. The methodology used in this work is a combination of first principles based on the density functional theory and effective Hamiltonians based on the group theory analysis. We construct a low energy model, using a base extracted from ab-initio results. Our combined first principles and space-group-dependent hamiltonian provides a power tool that can be extended to other finite-sized systems.