Investigação dos estados topologicamente protegidos em siliceno e germaneno

Abstract

The main objective of this work is to research and obtain surface protected topological states in nano-ribbons created from the leaves of Germanene and Silicene. These sheets belong to the class of Topological Insulators and correspond to monolayers of germanium and silicon atoms in a hexagonal arrangement that is similar to the graphene sheet. For this investigation, we conducted a study of the electronic and structural properties of these sheets, as well as their respective nano-ribbons through first-principles calculations based on density functional theory (DFT). In this methodology we use the generalized gradient approximation (GGA) for estimating the exchange and correlation term, and the PAW method for the effective potential and the expansion of plane waves of the Kohn-Sham. We conducted a computer simulation with the aid of the package VASP (Vienna ab-initio Simulation Package). As a starting point for our research, we used the methodology of solid state physics in order to describe the crystalline structure of the leaves as well as their mutual space. Subsequently we analyze the band structure, from which many of its properties can be visualized. For this task, we initially proceeded to investigate the stability of these systems via total energy calculations, in turn obtaining the network parameters that minimizes the energy of the system. We also obtained the energy cutoff, ECUT used in our calculations, or in other words, determining the number of plane waves needed to expand the electronic wave functions on the DFT formalism. We continued our study, with the creation and analysis of two different configurations of nano-ribbons, one that corresponds to a straightforward cut of the sheet with the armchair termination pattern, and the other based on a reconstruction of those edges, which provide an energetically more stable system. Subsequently we obtained electronic structures, and conducted a study of its variation due to the change of the width of the nano-ribbon and ionic relaxation of its edges. In a way, we modified the above parameters in order to obtain a system that would give us a zero gap, or at least insignificant, as well as a specific configuration for the spin texture, in order to verify the evidence of surface protected topological states in these nano-ribbons.