2-Dimensional (2D) materials are characterised by atomic thickness and significantly larger edge-lengths, producing particles which are highly confined in 1 direction. Reducing a material to one or few atomic layers gives rise to structural and electronic properties that deviate significantly from those of the bulk crystal. For this reason 2D nanosheets have been investigated for potential application in sensing, catalysis, capacitance, photovoltaics and for flexible circuits (among others).Despite rapid progress in understanding the synthesis and properties of 2D nanosheets in recent years, there remain significant problems surrounding the development of scalable production methods, understanding and tuning fundamental properties, and controlling the size and monodispersity of semiconductor crystals. In addition, new materials with novel properties are constantly sought in order to meet specific requirements. Although the tools developed over the last 12 years can often be applied to the fabrication of these materials, understanding their behaviour and limitations is ongoing. The following thesis discusses the routes to the fabrication of 2-dimensional materials and explores the production of MoS2, black phosphorus and tin(II) sulfide nanosheets. The aim of each piece of work is determined by the level of development of the field; MoS2 nanosheets have been known for several years and therefore the work presented was motivated by a desire to impart size control for specific applications. The study of phosphorene and 2D tin(II) sulfide is in its infancy; as such the focus remains on scalable nanosheet exfoliation and developing an understanding of their properties. The following studies on phosphorene report the exfoliation of nanosheets in organic and aqueous surfactant solutions and an investigation of the stability and breakdown products of the resulting colloidal suspensions. The stabilisation of phosphorene in aqueous media paves the way for its use in biological systems. Band-gap tuning in IV-VI analogues of phosphorene is demonstrated by size-selection of exfoliated SnS nanosheets. Although the physical characteristics of nanosheets and their incorporation into devices receive some attention, this thesis will focus mainly on the synthetic aspects of 2D materials research.

As a result of the computing power provided by the current technology, computational methods now play an important role in modeling and designing materials at the nanoscale. The focus of this dissertation is two-fold: first, new computational methods to model nanoscale transport are introduced, then state-of-the-art tools based on density functional theory are employed to explore the properties of phosphorene, a novel low dimensional material with great potential for applications in nanotechnology. A Wannier function description of the electron density is combined with a generalized Slater-Koster interpolation technique, enabling the introduction of a new computational method for constructing first-principles model Hamiltonians for electron and hole transport that maintain the density functional theory accuracy at a fraction of the computational cost. As a proof of concept, this new approach is applied to model polythiophene, a polymer ubiquitous in organic photovoltaic devices. A new low dimensional material, phosphorene - a single layer of black phosphorous - the phosphorous analogue of graphene was first isolated in early 2014 and has attracted considerable attention. It is a semiconductor with a sizable band gap, which makes it a perfect candidate for ultrathin transistors. Multi-layer phosphorene transistors have already achieved the highest hole mobility of any two-dimensional material apart from graphene. Phosphorene is prone to oxidation, which can lead to degradation of electrical properties, and eventually structural breakdown. The calculations reported here are some of the first to explore this oxidation and reveal that different types of oxygen defects are readily introduced in the phosphorene lattice, creating electron traps in some situations. These traps are responsible for the non-ambipolar behavior observed by experimental collaborators in air-exposed few-layer black phosphorus devices. Calculation results predict that air exposure of phosphorene creates a new family of two-dimensional oxides, which has been later confirmed by X-ray photoemission measurements. These oxides can form protective coatings for phosphorene and have interesting tunable electronic properties. Finally, Wannier function interpolation has been used to demonstrate that a saddle-point van Hove singularity is present near the phosphorene Fermi energy, as observed in some layered cuprate high temperature superconductors; this leads to an intriguing strain-induced ferromagnetic instability.

Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-17T19:58:30Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_CristianMafraLedur.pdf: 6580375 bytes, checksum: be466f19cd474caaa7ecaa4004ef38ba (MD5) / Made available in DSpace on 2018-08-17T19:58:30Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_CristianMafraLedur.pdf: 6580375 bytes, checksum: be466f19cd474caaa7ecaa4004ef38ba (MD5) Previous issue date: 2017-08-15 / The two-dimensional (2D) materials display many interesting properties, which are not found in bulk structure because the original electronic structure is substantially altered from its three-dimensional (3D) characteristics. Black and blue phosphorene are 2D materials which are attracting many fields interest because of their electronic and magnetic properties, making them possible materials for spintronics devices application. These nanomaterials display some characteristics that allow their use on sensors, thus, this work aims to evaluate the changes in black and blue phosphorenes’ electronic and magnetic properties, before and after the chemical groups functionalizations. We utilized the amide, amine, carboxyl and hydroxyl chemical groups because they are into many living organisms, directing the results for possible systems of molecules adsorption with chemical and/or biological interest application. First-principles calculations based on Density Functional Theory with the Local Density Approximation (LDA) were performed using the SIESTA code. Blue phosphorene systems show a higher structure disturbance level when functionalized, so as atoms displacement, when compared with black phosphorene respective systems. Its binding energy also presents higher values when compared to black phosphorene systems. Both configurations 1-2, show the more stable systems for carboxyl groups functionalized on black and blue phosphorenes, presenting a 2.34 and 2.72 eV binding energy, respectively. The configuration 1-2 take on this post because reestablish the systems' symmetry. The symmetry reestablishment effect occurs in every kind of chemical group. These results imply in a promising black and blue phosphorenes application in systems of molecules adsorption with chemical and/or biological interest. / Diversas estruturas bidimensionais (2D) vêm apresentando propriedades interessantes, pois as mesmas são substancialmente alteradas quando comparadas às suas formas tridimensionais (3D). As estruturas de fosforeno negro e azul são materiais 2D que atraíram o interesse de muitas áreas pelo fato de suas propriedades eletrônicas e magnéticas indicarem o seu possível uso em dispositivos spintrônicos. Esses nanomateriais possuem características que permitem sua utilização em sensores, desta forma, este trabalho visa avaliar as mudanças nas propriedades eletrônicas e estruturais dos fosforenos causadas pelas funcionalizações dos grupos químicos amida, amina, carboxila e hidroxila, os quais compõem grande parte das moléculas biológicas presentes em organismos vivos para possível aplicação em sistemas de adsorção de moléculas de interesse biológico. Para desenvolver este trabalho fez-se uso de simulação computacional com cálculos de primeiros princípios, utilizando a Teoria do Funcional da Densidade (DFT), e Aproximação Local da Densidade (LDA) implementada no código computacional SIESTA. Este estudo demonstra que a estrutura de fosforeno azul apresenta maiores perturbações estruturais, como a modificação da posição inicial dos átomos de fósforo, devido às funcionalizações dos grupos químicos, se comparado aos sistemas funcionalizados com o fosforeno negro. Outro fator que chama a atenção são os valores de energia de ligação, onde todos os sistemas de fosforeno azul apresentam módulos maiores neste parâmetro para as respectivas configurações de funcionalização de grupos químicos. Os sistemas mais estáveis de fosforeno negro e azul funcionalizados com dois grupos carboxílicos apresentaram 2,34 e 2,72 eV, respectivamente, para a energia de ligação. Estes sistemas apresentam maior estabilidade devido ao fato de que restabelecem a simetria do sistema, em comparação com as outras configurações. Efeitos semelhantes ocorrem para todos os grupos químicos funcionalizados. Estes resultados indicam uma promissora aplicação das estruturas de fosforeno negro e azul como sistemas de adsorção de moléculas de interesse químico e/ou biológico.

The control of low dimensional materials holds potential for revolutionizing the electronic, thermal, and thermoelectric materials engineering. Through strategic manipulation and optimization of these materials, unique properties can be uncover which enable more efficient and effective materials development. Towards the determination of nanoscale strategies to improve the electronic and phononic devices, computational simulations of modified low dimensional materials have been carried in this research. First, the electronic properties of chemically func tionalized phosphorene monolayers are evaluated with spin-polarized Density Functional Theory, as a potential method to tune their electronic properties. The functionalization not only leads to formation of additional states within the semiconducting gap, but also to the emergence of local magnetism. The magnetic ground state and electronic structure are investigated in dependence of molecular coverage, lattice direction of the molecular adsorption and molecule type functionalization. Furthermore, the physical and transport properties of phosphorene grain boundaries under uniaxial strain are evaluated by the use of Density Functional based Tight Binding method in combination with Landauer theory. In both grain boundary types, the electronic bandgap decreases under strain, however, the respective thermal conductance is only weakly affected, despite rather strong changes in the frequency-resolved phonon transmission. The combination of both effects results in an enhancement in the thermoelectric figure of merit in the phosphorene grain boundary systems. Finally, the thermoelectric properties of carbon nanotubes peapod heterostructures are studied and compared to pristine nanotubes using also the Density Functional based Tight Binding method and Landauer theory. It is found that the fullerene encapsulation modifies the electron and phonon transport properties, causing the formation of electronic channels and the suppression of vibrational modes that lead to an improvement of the thermoelectric figure of merit. The results of this thesis highlight the potential of strategic manipulation and optimization of low dimensional materials in improving their unique electronic and thermal properties, revealing promising avenues for improving electronic and phononic devices.:ABSTRACT i ZUSAMMENFASSUNG ii ACKNOWLEDGEMENT iv LIST OF FIGURES ix LIST OF TERMS AND ABBREVIATIONS xviii 1 Introduction 1 1.1 Motivation 1 1.2 Objectives and outline 6 2 Computational Methods 8 2.1 Density Functional Theory 8 2.1.1 The Many-Body System Hamiltonian and the Born-Oppenheimer approximation 9 2.1.2 Thomas-Fermi-Dirac approximation model 10 2.1.3 The Hohenberg-Kohn theorems 12 2.1.4 The Kohn-Sham orbitals equations 13 2.1.5 Exchange-correlation functionals 15 2.2 Density Functional Based Tight Binding method 16 2.2.1 Tight-binding formalism 17 2.2.2 From DFT to DFTB 20 2.2.3 Parametrization 22 2.3 Atomistic Green’s functions 23 2.3.1 Non-Equilibrium Green’s functions for modeling electronic transmission 23 2.3.2 Non-equilibrium Green’s function for modeling thermal transmission 27 3 Tuning the electronic and magnetic properties through chemical functionalization 3.1 Introduction 33 3.1.1 Black phosphorus as a 2D material 33 3.1.2 Chemical Functionalization of low dimensional systems 35 3.1.3 Bipolar Magnetic Semiconductors 36 3.2 Computational approach 38 3.3 Interface effects in phosphorene by OH functionalization 39 3.3.1 Single molecule functionalization 39 3.3.2 Lattice selection 43 3.3.3 Coverage 45 3.4 Chiral functionalization effect in phosphorene 48 3.5 Functionalizing phosphorene towards BMS 51 3.6 Summary 53 4 Tuning transport properties through strain and grain bound-aries 4.1 Introduction 54 4.1.1 Strain in low dimensional materials 54 4.1.2 Grain boundaries 56 4.2 Computational approach 58 4.2.1 Molecular systems 58 4.2.2 Electron and phonon transport and thermoelectric figure of merit 58 4.3 Structural modification by strain in GB systems 60 4.4 Electronic structure modification by strain in GB systems 63 4.5 Thermal transport modification by strain in GB systems 65 4.6 Thermoelectric figure of merit of strained GB systems 68 4.7 Summary 71 5 Tuning transport properties through hybrid nanomaterials: CNT peapods 73 5.1 Introduction 73 5.1.1 Carbon-based nanostructures 73 5.1.2 CNT peapods as hybrid nanomaterials 76 5.2. Computational details 77 5.2.1 CNT peapod model 77 5.2.2 Quantum transport methodology 78 5.3 Structural properties of CNT peapods 79 5.4 Electronic properties of CNT peapods 80 5.5 Thermal properties of CNT peapods 83 5.6 Thermoelectronic properties of CNT peapods 85 5.7 Summary 88 6 Conclusions and outlook 91 Appendices Appendix A Supplementary information to phosphorene functionalization A.1 Spin resolved density of states of 1-OH system 96 A.2 Spin valve model 97 Appendix B Supplementary information to phosphorene grain boundaries 98 B.1 Projected Phonon Density of States in GB1 98 B.2 Thermoelectric transport properties of GB2 99 Appendix C Supplementary information to CNT peapods 101 C.1 Geometry optimization of CNT peapods with larger CNT diameter 101 C.2 Additional analysis of electron transport properties 102 C.3 Phonon band structure of different CNT structures 104 C.4 Additional analysis of thermoelectric performance 105 REFERENCES 105 LIST OF PUBLICATIONS 131 PRESENTATIONS 132 / Die Kontrolle niedrigdimensionaler Materialien birgt das Potenzial für eine Revolutionierung der elektronischen, thermischen und thermoelektrischen Technologien. Durch strategische Manipulation und Optimierung dieser Materialien können einzigartige Eigenschaften aufgedeckt werden, die eine effizientere und effektivere Materialentwicklung ermöglichen. Um Strategien im Nanobereich zur Verbesserung elektronischer und phononischer Bauelemente zu ermitteln, wurden in dieser Forschungsarbeit rechnerische Simulationen modifizierter niedrigdimensionaler Materialien durchgeführt. Zunächst werden die elektronischen Eigenschaften von chemisch funktionalisierten Phosphoren-Monoschichten mit Hilfe der spinpolarisierten Dichtefunktionaltheorie als potenzielle Methode zur Abstimmung ihrer elektronischen Eigenschaften bewertet. Die Funktionalisierung führt nicht nur zur Bildung zusätzlicher Zustände innerhalb der halbleitenden Lücke, sondern auch zum Auftreten von lokalem Magnetismus. Der magnetische Grundzustand und die elektronische Struktur werden in Abhängigkeit von der molekularen Bedeckung, der Gitterrichtung der molekularen Adsorption und der Funktionalisierung des Moleküls untersucht. Darüber hinaus werden die Transporteigenschaften von Phosphoren-Korngrenzen unter uniaxialer Belastung mit Hilfe der auf Dichtefunktionen basierenden Tight-Binding-Methode in Kombination mit der Landauer-Theorie untersucht. In beiden Korngrenzentypen nimmt die elektronische Bandlücke unter Dehnung ab, die jeweilige Wärmeleitfähigkeit wird jedoch nur schwach beeinflusst, trotz ziemlich starker Änderungen in der frequenzaufgelösten Phononentransmission. Die Kombination bei der Effekte führt zu einer Erhöhung der thermoelektrischen Leistungszahl in den Phosphorkorngrenzensystemen. Schließlich werden die thermoelektrischen Eigenschaften von Kohlenstoffnanoröhren-Peapod-Heterostrukturen untersucht und mit denen von reinen Nanoröhren verglichen, wobei auch die auf Dichtefunktionen basierende Tight-Binding-Methode und die Landauer-Theorie verwendet werden. Es wird festgestellt, dass die Fullereneinkapselung die Elektronen- und Phononentransporteigenschaften modifiziert und die Bildung von elektronischen Kanälen und die Unterdrückung von Schwingungsmoden bewirkt, was zu einer Verbesserung der thermoelektrischen Leistungszahl führt. Die Ergebnisse dieser Arbeit verdeutlichen das Potenzial der strategischen Manipulation und Optimierung niedrigdimensionaler Materialien zur Verbesserung ihrer einzigartigen elektronischen und thermischen Eigenschaften und zeigen vielversprechende Wege zur Verbesserung elektronischer und phononischer Bauteile auf.:ABSTRACT i ZUSAMMENFASSUNG ii ACKNOWLEDGEMENT iv LIST OF FIGURES ix LIST OF TERMS AND ABBREVIATIONS xviii 1 Introduction 1 1.1 Motivation 1 1.2 Objectives and outline 6 2 Computational Methods 8 2.1 Density Functional Theory 8 2.1.1 The Many-Body System Hamiltonian and the Born-Oppenheimer approximation 9 2.1.2 Thomas-Fermi-Dirac approximation model 10 2.1.3 The Hohenberg-Kohn theorems 12 2.1.4 The Kohn-Sham orbitals equations 13 2.1.5 Exchange-correlation functionals 15 2.2 Density Functional Based Tight Binding method 16 2.2.1 Tight-binding formalism 17 2.2.2 From DFT to DFTB 20 2.2.3 Parametrization 22 2.3 Atomistic Green’s functions 23 2.3.1 Non-Equilibrium Green’s functions for modeling electronic transmission 23 2.3.2 Non-equilibrium Green’s function for modeling thermal transmission 27 3 Tuning the electronic and magnetic properties through chemical functionalization 3.1 Introduction 33 3.1.1 Black phosphorus as a 2D material 33 3.1.2 Chemical Functionalization of low dimensional systems 35 3.1.3 Bipolar Magnetic Semiconductors 36 3.2 Computational approach 38 3.3 Interface effects in phosphorene by OH functionalization 39 3.3.1 Single molecule functionalization 39 3.3.2 Lattice selection 43 3.3.3 Coverage 45 3.4 Chiral functionalization effect in phosphorene 48 3.5 Functionalizing phosphorene towards BMS 51 3.6 Summary 53 4 Tuning transport properties through strain and grain bound-aries 4.1 Introduction 54 4.1.1 Strain in low dimensional materials 54 4.1.2 Grain boundaries 56 4.2 Computational approach 58 4.2.1 Molecular systems 58 4.2.2 Electron and phonon transport and thermoelectric figure of merit 58 4.3 Structural modification by strain in GB systems 60 4.4 Electronic structure modification by strain in GB systems 63 4.5 Thermal transport modification by strain in GB systems 65 4.6 Thermoelectric figure of merit of strained GB systems 68 4.7 Summary 71 5 Tuning transport properties through hybrid nanomaterials: CNT peapods 73 5.1 Introduction 73 5.1.1 Carbon-based nanostructures 73 5.1.2 CNT peapods as hybrid nanomaterials 76 5.2. Computational details 77 5.2.1 CNT peapod model 77 5.2.2 Quantum transport methodology 78 5.3 Structural properties of CNT peapods 79 5.4 Electronic properties of CNT peapods 80 5.5 Thermal properties of CNT peapods 83 5.6 Thermoelectronic properties of CNT peapods 85 5.7 Summary 88 6 Conclusions and outlook 91 Appendices Appendix A Supplementary information to phosphorene functionalization A.1 Spin resolved density of states of 1-OH system 96 A.2 Spin valve model 97 Appendix B Supplementary information to phosphorene grain boundaries 98 B.1 Projected Phonon Density of States in GB1 98 B.2 Thermoelectric transport properties of GB2 99 Appendix C Supplementary information to CNT peapods 101 C.1 Geometry optimization of CNT peapods with larger CNT diameter 101 C.2 Additional analysis of electron transport properties 102 C.3 Phonon band structure of different CNT structures 104 C.4 Additional analysis of thermoelectric performance 105 REFERENCES 105 LIST OF PUBLICATIONS 131 PRESENTATIONS 132

The intent of this thesis is to improve upon previously proposed tight-binding models for one dimensional black phosphorus, or phosphorene. Previous models offer only a qualitative analysis of the band structure of phosphorene, and fail to fully realize critical elements in the electronic band structure necessary for transport calculations. In this work we propose an improved tight-binding model for phosphorene by including up to eight nearest-neighbor interactions. The efficacy of the model is verified by comparison with DFT-HSE06 calculations, and the anisotropy of the effective masses in the armchair and zigzag directions is considered.

Our vision is as yet unsurpassed by machines because of the sophisticated representations of objects in our brains. This representation is vastly different from a pixel-based representation used in machine storages. It is this sophisticated representation that enables us to perceive two faces as very different, i.e, they are far apart in the “perceptual space”, even though they are close to each other in their pixel-based representations. Neuroscientists have proposed distances between responses of neurons to the images (as measured in macaque monkeys) as a quantification of the “perceptual distance” between the images. Let us call these neuronal dissimilarity indices of perceptual distances. They have also proposed behavioural experiments to quantify these perceptual distances. Human subjects are asked to identify, as quickly as possible, an oddball image embedded among multiple distractor images. The reciprocal of the search times for identifying the oddball is taken as a measure of perceptual distance between the oddball and the distractor. Let us call such estimates as behavioural dissimilarity indices. In this thesis, we describe a decision-theoretic model for visual search that suggests a connection between these two notions of perceptual distances. In the first part of the thesis, we model visual search as an active sequential hypothesis testing problem. Our analysis suggests an appropriate neuronal dissimilarity index which correlates strongly with the reciprocal of search times. We also consider a number of alternative possibilities such as relative entropy (Kullback-Leibler divergence), the Chernoff entropy and the L1-distance associated with the neuronal firing rate profiles. We then come up with a means to rank the various neuronal dissimilarity indices based on how well they explain the behavioural observations. Our proposed dissimilarity index does better than the other three, followed by relative entropy, then Chernoff entropy and then L1 distance. In the second part of the thesis, we consider a scenario where the subject has to find an oddball image, but without any prior knowledge of the oddball and distractor images. Equivalently, in the neuronal space, the task for the decision maker is to find the image that elicits firing rates different from the others. Here, the decision maker has to “learn” the underlying statistics and then make a decision on the oddball. We model this scenario as one of detecting an odd Poisson point process having a rate different from the common rate of the others. The revised model suggests a new neuronal dissimilarity index. The new dissimilarity index is also strongly correlated with the behavioural data. However, the new dissimilarity index performs worse than the dissimilarity index proposed in the first part on existing behavioural data. The degradation in performance may be attributed to the experimental setup used for the current behavioural tasks, where search tasks associated with a given image pair were sequenced one after another, thereby possibly cueing the subject about the upcoming image pair, and thus violating the assumption of this part on the lack of prior knowledge of the image pairs to the decision maker. In conclusion, the thesis provides a framework for connecting the perceptual distances in the neuronal and the behavioural spaces. Our framework can possibly be used to analyze the connection between the neuronal space and the behavioural space for various other behavioural tasks.

No description available.

This thesis is devoted to the optical properties of low-dimensional structures based on such two-dimensional materials as graphene, silicene and phosphorene. We investigate optical properties of a variety of quasi-one dimensional and quasi-zero-dimensional structures, which are promising for future optoelectronics. Primarily we focus on their low-energy optical properties and how these properties are influenced by the structures’ geometry, external fields, intrinsic strain and edge disorder. As a consequence of this endeavor, we find several interesting effects such as correlation between the optical properties of tubes and ribbons whose periodic and ‘hard wall’ boundary conditions are matched and a universal value of matrix element in narrow-gap tubes and ribbons characterizing probability of transitions across the band gap opened up by intrinsic strain originating from the tube’s surface curvature or ribbon’s edge relaxation. The analytical study of the gapped 2D Dirac materials such as silicene and germanene, which have some similarity to the aforementioned quasi-one-dimensional systems in terms of physical description, reveals a valley- and polarization-dependent selection rules. It was also found that absorption coefficient should change in gapped materials with increasing frequency and become a half of its value for gap edge transitions when the spectrum is linear. Our analysis of the electronic properties of flat clusters of silicene and phosphorene relates the emergence and the number of the peculiar edge states localized at zero energy, so-called zero-energy states, which are know to be of topological origin, to the cluster’s structural characteristics such as shape and size. This allows to predict the presence and the number of such states avoiding complicated topological arguments and provides a recipes for design of metallic and dielectric clusters. We show that zero-energy states are optically active and can be efficiently manipulated by external electric field. However, the edge disorder is important to take into account. We present a new fractal-based methodology to study the effects of the edge disorder which can be applied also to modeling of composite materials. These finding should be useful in design of optoelectronic devices such as tunable emitters and detectors in a wide region of electromagnetic spectrum ranging form the mid-infrared and THz to the optical frequencies.

Submitted by ARMANDO ARQUIMEDES PEZO LOPEZ (armandopezo333@gmail.com) on 2017-09-15T18:49:05Z No. of bitstreams: 1 pezo_a_ms_ift.pdf: 7486652 bytes, checksum: 7101195a7ca026fe9e98885ba89961f1 (MD5) / Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-09-19T17:23:53Z (GMT) No. of bitstreams: 1 pezolopez_aa_me_ift.pdf: 7486652 bytes, checksum: 7101195a7ca026fe9e98885ba89961f1 (MD5) / Made available in DSpace on 2017-09-19T17:23:53Z (GMT). No. of bitstreams: 1 pezolopez_aa_me_ift.pdf: 7486652 bytes, checksum: 7101195a7ca026fe9e98885ba89961f1 (MD5) Previous issue date: 2016-08-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A realização experimental do grafeno em 2004 abriu as portas para os estudos de uma nova geração de materiais, estes chamados materiais bidimensionais são a expressão final do que poderíamos pensar em material plano (monocamada) que, eventualmente, podem ser empilhados para formar o bulk. O grafeno oferece uma grande variedade de propriedades físicas, em grande parte, como o resultado da dimensionalidade de sua estrutura, e pelas mesmas razões, materiais como Fosforeno (P), Siliceno (S), Nitreto de Boro hexagonal (hBN), dicalcogenos de metais de transição (TMDC), etc. São muito interessantes para fins teóricos, como para futuras aplicações tecnológicas que podem-se desenvolver a partir deles, como dispositivos de spintrônica e armazenamento. Neste trabalho o estudo desenvolvido são as propriedades eletrônicas dos materiais apresentados acima (grafeno, fosforeno e MoTe 2 ), e além disso, ja que o acoplamento spin-órbita aumenta à medida que o número atômico tambem aumenta, espera-se que este parâmetro desempenhe um papel na estrutura eletrônica, particularmente para os TMDC’s. Começamos descrevendo genéricamente esses três sistemas, isto é, para o grafeno, podemos usar uma abordagem tipo tight binding, a fim de encontrar a dispersão de energia para as quase-particulas perto do nível de Fermi (Equação de Dirac). Usando cálculos DFT estudou-se de forma geral as propriedades desses sistemas com a inclusão do espin órbita. Abordou-se cálculos para descrever os efeitos do acoplo spin órbita sobre os materiais isolados, tambem nas heterostruturas (duas camadas formadas por eles). Finalmente, tambem estudou-se a possibilidade de defeitos e sua possível influência sobre a estrutura eletrônica das heterostruturas. / The experimental realization of graphene in 2004 opened the gates to the studies of a new generation of materials, these so-called 2 dimensional materials are the final expression of what we could think of a plane material (monolayer) that eventually can be stacked to form a bulk. Graphene, the wonder material, offers a large variety of physical properties, in great part, as the result of the dimensionality of its structure, and for the same reasons, materials like phosphorene(P), silicene(S), hexagonal Boron Nitride (hBN), transition metal dichalcogenides(TMDC), etc. are very interesting for theoretical purposes, as for the future technological applications that we can develope from them, such as Spintronics and Storage devices. In this dissertation we theoretically study the electronic properties of the materials presented above (graphene, Phosphorene and MoTe2), and besides that, since the spin-orbit coupling strength increases as the atomic number does, we expect that this paremeter plays a role in the electronic structure, particularly for the TMDC. We start describing generically those three systems using density functional theory including the effect of spin orbit. We address calculations to describe the effects of spin orbit on the isolated materials as well as the heterostructures. Finally we also include the possibility of defects in graphene and their possible influence on the electronic structure of heterostructures.