Simulação computacional aplicada à física dos materiais: fases topológicas em sistemas 2D - Lima, Felipe David Crasto de (2020)
Throughout this work we explore new two-dimensional lattices constructed from the Archimedean tiling of the plane, characterizing its band structure and topological quantum spin Hall phases. As a proof of principle, within a combination of density functional theory and effective Hamiltonians, we have explored the material realization of Archimedean lattices. Fist, focusing in the kagome lattice, we predict within magnetic metal-organic frameworks the arising of quantum anomalous Hall effects. Additionally, from the time reversal symmetric counterpart, i.e. quantum spin Hall effect, we include a new multilayer degree of freedom into the control of metal-organic frameworks electronic properties. Within this multilayer system a layer localization effect of the topological states can be controlled through a external electric field. Focusing in a different Archimedean lattice, we shown its material realization in a two-dimensional boron allotrope. This material presents linear dispersive Dirac fermions in a px/py orbital pseudospin subspace. Here we shown a helical behavior of these orbital pseudospinors, i.e., its direction locked with the momentum direction, in a analogous way as the three dimensional topological insulator surface states. Furthermore, by adding a layer degree of freedom in addition to the orbital one, i.e., stacking of borophene bilayers, allows a control of the orbital texture by engineering the stacking order and external electric field. Lastly, we explored the construction of high-degeneracy points, which are not predicted by space-group symmetries. Here we show that pair permutation symmetries stabilizes such points, which are presents in a two Archimedean lattices, but also in other 3D lattices. We have found the recipe for constructing such lattices, where its experimental realization was proposed in metal lattices designed over silicon carbide surface oxidized by a ordered silica phase. In such systems, the post-transition metals s orbitals give rise to surface states localized neatly within the substrate’s semiconducting energy gap.