O principal objetivo da spintrÖnica Ä entender os mecanismos que permitem controlar de forma eficiente tanto a configuraìïo de spin quanto as correntes de spin, orientando ao uso do grau de liberdade do spin como o elemento bçsico de dispositivos digitais. Por exemplo, o ?transistor spintrÖnico, no qual o "ON" e o "OFF" sïo definidos pela orientaìïo do spin. Muitos destes mecanismos propostos estïo baseados na geraìïo de corrente de spin em semicondutores tipo Rashba e isolantes topolùgicos (TIs) usando a interaìïo spin-ùrbita e campos elÄtricos. No entanto, embora os TIs apresentam estados de borda ou superfÆcie protegidos contra a desordem por uma certa simetria, os sistemas que tÉm sido propostos sïo muito sensÆveis aos processos de fabricaìïo, impurezas e efeitos de temperatura; de fato, nïo Ä trivial observar os fenÖmenos conhecidos ou inclusive obter experimentalmente o transporte de spin dominado pelos estados topologicamente protegidos. Nesta tese, usando cçlculos de primeiros princÆpios, modelos "tight-binding" e cçlculos de invariantes topolùgicos, foi proposta uma possÆvel soluìïo para estes problemas, nïo somente para predizer novos TIs de forma sistemçtica, mas tambÄm para sugerir novos fenÖmenos que permitam controlar as correntes de spin. Especificamente, i) exploramos a famÆlia de sistemas similares ao grafeno, propondo uma nova classe de inversïo de banda; ii) usando aprendizado de mçquina prevemos de forma sistemçtica novos TIs; iii) encontramos que os estados de bulk poderiam tambÄm ser protegidos pela simetria de reversïo temporal, e nïo necessariamente a procura deve ser focada em encontrar matÄrias com gap grande; iv) encontramos que um campo elÄtrico quebrando a simetria de espelho em isolantes topolùgicos duais permite controlar a polarizaìïo de spin, levando a uma geraìïo nïo dinëmica de spin o qual permitiria a construìïo de um transistor spintrÖnico; e v) estudamos a influencia dos estados de Bulk no transporte de estados de superfÆcie. Neste estudo, implementamos os invariantes topolùgicos: n£mero de Chern e invariante Z$_2$ nos cùdigos SIESTA, VASP e AIMS usados para cçlculos de primeiros princÆpios. TambÄm implementamos um modelo para o transporte eletrÖnico usando spin-ùrbita. Acreditamos que nosso trabalho ajuda no entendimento das propriedades dos TIs, dos efeitos de campos elÄtricos externos e as possÆveis aplicaì¢es para dispositivos. TambÄm acreditamos que nossa proposta, o controle da polarizaìïo de spin quebrando a simetria de espelho, poderia abrir uma nova çrea de estudo em TIs.

The main goal of spintronics is to understand the mechanisms to efficiently control both spin configurations and spin currents, aiming the use of the spin degree of freedom as the basic element of digital devices, e.g., the "spintronic transistor" in which the ON and OFF are defined by the spin electron orientation. Many of the most promising proposed mechanisms are based on spin current generation in Rashba and/or topological semiconductors mainly mediated by the spin-orbit coupling and electric fields. However, despite topological insulators (TIs) are predicted to feature boundary (surface/edge for three/two dimensional systems) states protected by a given symmetry against disorder, the proposed TI candidates are extremely sensitive to fabrications processes, impurities, and temperature effects; indeed, it is difficult to observe the current known phenomena or even to experimentally achieve the spin transport regime governed by the topologically protected boundary states. In this thesis, based on first-principle calculation, tight-binding models and topological invariant calculations we propose possible solutions for these problems, not only systematically predicting new topological insulator candidates with suitable conditions to achieve the boundary states transport regime, but also suggesting novel phenomena allowing for the spin current control. Specifically, we have i) explored the honeycomb-lattice family proposing a new kind of band inversion; ii) used machine learning to systematically predict new two-dimensional TIs; iii) proposed that instead of focused on finding TIs exhibiting large band gaps, the bulk states can be intrinsically protected by the time-reversal symmetry; iv) found that an external electric field breaking the mirror symmetry in dual topological insulators can be used to control the spin polarization, leading to a non-dynamic spin-polarization generation and allowing the construction of a spintronic transistor; and v) studied the influence of the bulk states in the surface electronic transport. To address this issues we have also implemented the topological invariants: Chern Number Cn and the Z2 invariant within the SIESTA, VASP and AIMS codes which are used to performed first-principles calculations, and we made a model for the electronic transport considering spin-orbit coupling. We believe that our work advances the understanding of the properties of TIs, the external field effects in these systems, and their potential for device applications. We also believe that our proposal, i.e., the spin-polarization controlled by the mirror symmetry breaking, could open a new research area in TIs.