Estudo por primeiros princípios da estrutura eletrônica de redes covalente-orgânicas e metal-orgânicas

Abstract

In this work, we investigated, through a combination of analytical and first principles methods, the electronic properties of bidimensional metal-organic frameworks (MOFs) and covalent-organic frameworks (COFs). Firstly, we formulate a model consisting of superposition of the kagomé (K) and honeycomb (H) lattices: the KH lattice, with a HamiltonianthatreproducesthebandsneartheFermilevelofseveralCOFsandMOFs:the COF family proposed by Jean-Joseph et al; the Cu3(HITP)2 MOF, which were synthesized in bulk and thin film forms; the Ni3C12S12 MOF, which were synthesized in 2D form on HOPG. Besides that, the inclusion of the intrinsic spin-orbit term on the Hamiltonian of the KH lattice predicts the gap opening obtained through first principles calculations. We also show that the partial inclusion of the exact exchange functional leads to modifications on the bands of the Ni3C12S12 and the new family of 2D MOFs M3(THT)2, considering M=Ni, which were synthesized in 2D form on SiO2 and M=Pt, which were synthesized in bulk form. Considering M=Cu and Au, their electronic structures are independent with the change on the functional. Among the MOFs presented here, most present spin-orbit coupling induced band gaps, which is a key ingredient to realize the properties of a topological insulator. In this context, we investigated the topological properties of the 2D MOF Ni3C12S12, which is a topological insulatoruponelectrostaticdopingoftwoelectronsperunitcell.Wealsoconsideredinthis structure the change of all Ni atoms to Pt atoms, which leads to a significant enhancement of the spin-orbit gap. Besides that, we propose that bilayers structures produced by the stackingoftwoidenticallayersofNi3C12S12 orPt3C12S12 alsoleadtotopologicalinsulators upon electrostatic doping of two electrons per unit cell. The electronic structures of these bilayers systems is characterized by a non-trivial gap between graphene-like bands, akin to the model proposed by Kane and Mele. Beyond the analysis of the topological invariants, we investigate the band structures of ribbons produced from the the monolayer and bilayers structures of the Ni3C12S12 and Pt3C12S12 . Our results suggest that topological protected chiral edge states emerge at the edges of the ribbons, and these states reside within the non-trivial spin-orbit coupling induced band gaps. Surprisingly, in some cases these states occur even for thin ribbons relative to the size of the 2D structures’ unit cells. Further, we show that tight-binding models for ribbons produced from kagomé and honeycomb lattices reproduce the results obtained through first principles methods. Considering the bilayers structures, we highlight that the band structures of the ribbons are a realization of the Kane and Mele model for a honeycomb ribbon with zigzag edge. Considering the bilayers structures, it is interesting to analyze the case where the space inversion symmetry is broken due to a external electric fields. In this part, we show that the broken symmetry leads to Bychkov-Rashba-type splitting on the band structures of the bilayers systems. Again, this phenomenology is described by the Kane and Mele model with an extrinsic spin-orbit Rashba term on the tight-binding Hamiltonian.