Efeito de tamanho finito em isolantes topológicos Z₂ com um termo de acoplamento devido as interações entre segundos e terceiros vizinhos em diferentes tipos de bordas

Abstract

Topological insulators are material electronic that possess a gap of energy in the states of bulk as a conventional insulator, but possess edge states that allow the current conduction which are invariant under small deformation of the material. These states are possible because of a combination of strong spin-orbit interactions and time reversal symmetry. The model that we use to describe the Z₂ topological insulators is constituted by a model strong binding under a square lattice, where each site on the network contains two orbital, being that, a orbital has odd parity and the other has even parity. The orbital with odd parity has a higher energy than the orbital with even parity. This model is a simplification of the Bernevig-Hughes-Zhang model for quantum wells that have recently attracted much attention for realization of twodimensional topological insulators with protected helicoidal states of edge. We investigated the effect of finite size in two-dimensional Z2 topological insulator with interactions between first, second and third neighbors. For this, we use a tight-binding model which shows the existence of helical edge states. This model is characterized by a mass term M(k) = Δ - Bk², that is modified in accordance with the variation of parameters of interactions between second and third neighbors, so modifying the region where the material behaves as an insulator trivial or a topological insulator. Through the solution of tight-binding Hamiltoniana for a geometry of strip of finite width, We observe that the helicoidal edge on both sides of the spectrum of energy can couple together thus producing a gap of energy. The interaction between second and third neighbors modifies the size of the gap that spectrum. Analyzing the effect of finite size on the modes of edge of a topological insulator, we noticed that, the cadenciado increase of the parameters of interactions between the seconds and third neighbors, causes a gradual modification in the dispersion relation for a Z₂ topological insulator, which bring contributions to the spectrum, thus modifying the region where the material is insulation.