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Two-Dimensional (2D) materials often exhibit distinguished properties as compared to their 3D counterparts and offer great potential to advance technology. However, even graphene, the first synthesized 2D material, still faces several challenges, despite its high mobility and high thermal conductivity. Similarly, germanene and silicene face challenges due to readily available semiconducting properties to be used in electronics, photonics or photocatalysis applications. Here, we propose two approaches to tune the band gap: One is by forming nanoribbon and edge functionalization and another by doping using inorganic nanoparticle’s interaction with 2D nanomaterials. Edge functionalization of armchair germanene nanoribbons (AGeNRs) has the potential to achieve a range of band gaps. The edge atoms of AGeNRs are passivated with hydrogen (-H and -2H) or halogen (-F, -Cl,-OH, -2F,-2Cl) atoms. Using density functional theory calculations, we found that edge-functionalized AGeNRs had band gaps as small as 0.012 eV when functionalized by -2H and as high as 0.84 eV with -2F. Doping can change the semiconducting behavior of AGeNRs to metal due to the half-filled band making it useful for negative differential resistance (NDR) devices. In the case of zigzag germanene nanoribbons (ZGeNRs), single N or B doping transformed them from anti-ferromagnetic (AFM) semiconducting to ferromagnetic (FM) semiconductor or half-metal. Lastly, formation and edge free energy studies revealed the feasibility of chemical synthetization of edge-functionalized and doped germanene. Electronic, optical and transport properties of the graphene/ZnO heterostructure have been explored using first-principles density functional theory. The results show that Zn12O12 can open a band gap of 14.5 meV in graphene, increase its optical absorption by 1.67 times, covering the visible spectrum and extended to the infra-red (IR) range, and create slight nonlinear I-V characteristics depending on the applied bias. This agrees well with collaborative experimental measurement of a similar system. In conclusion, we have successfully studied the potential use of edge functionalization, band gap periodicity in nanoribbon width, and doping in germanene nanoribbons. Structural stability was also studied to investigate the feasibility for experimental synthesization. Inorganic nanoparticle’s interaction with graphene envisages the possibility of fabricating photo-electronic device covering visible spectrum and beyond. Finally, graphene complexes were merged with naturally available direct band gap of monolayer MoS2 to build efficient energy harvesting and photo detecting devices.

Quantum dots exhibit strongly size-dependent optical and electrical properties. The ability to join the dots into complex assemblies creates many opportunities for scientific discovery. This motivated our present research work on QDIPs, DWELLs, and graphene like QDs. The intention of this research was to study the size dependent achievements of QDIPs, DWELLs, and graphene like QDs with those of competitive technologies, with the emphasis on the material properties, device structure, and their impact on the device performance. In this dissertation four research studies pertaining to optical properties of quantum dot and dot-in-a-well infrared photodetectors, I-V characteristics of graphene quantum dots, and energy and spin texture of germanene quantum dots are presented. Improving self-assembled QD is a key issue in the increasing the absorption and improving the performance. In the present research work, an ideal self-assembled QD structure is analyzed theoretically with twenty-hole levels (Intraband optical transitions within the valence band) and twenty-electron energy levels (DWELL). Continuing the efforts to study self-assembled QDs we extended our work to graphene like quantum dots (graphene and germanene) to study the electronic transport properties. We study numerically the intraband optical transitions within the valence band of InxGa1-xAs/GaAs pyramidal quantum dots. We analyze the possibility of tuning of corresponding absorption spectra by varying the size and composition of the dots. Both ‘x ’ and the size of the quantum dot base are varied. We have found that the absorption spectra of such quantum dots are more sensitive to the in-plane incident light. We present numerically obtained absorption optical spectra of n-doped InAs/In0.15Ga0.85As/GaAs quantum dot-in-a-well systems. The absorption spectra are mainly determined by the size of the quantum dot and have weak dependence on the thickness of the quantum well and position of the dot in a well. The dot-in-a-well system is sensitive to both in-plane and out-of-plane polarizations of the incident light with much stronger absorption intensities for the in-plane-polarized light. We also present theoretically obtained I-V characteristics of graphene quantum dots, which are realized as a small piece of monolayer graphene. We describe graphene within the nearest-neighbor tight-binding model. The current versus the bias voltage has typical step-like shape, which is due to discrete energy spectrum of the quantum dot. The current through the dot system also depends on the position of the electrodes relative to the quantum dot. In relation to graphene quantum dots, we present our study of buckled graphene-like materials, like germanene and silicene. We consider theoretically germanene quantum dot, consisting of 13, 27, and 35 germanium atoms. Due to strong spin-orbit interaction and buckled structure of the germanene layer, the direction of the spin of an electron in the quantum dot depends on both the electron energy and external perpendicular electric field. With variation of energy, the direction of spin changes by approximately 4.50. Application of external electric field results in rotation of electron spin by approximately 0.50, where the direction of rotation depends on the electron energy.

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.

Na busca de um melhor entendimento das propriedades eletrônicas e magnéticas dos isolantes topológicos nos deparamos com uma das suas caraterísticas mais marcantes, a existência de estados de superfície metálicos com textura helicoidal de spin os quais são protegidos de impurezas não magnéticas. Na superfície estes canais de spin possuem um potencial enorme para aplicações em dispositivos spintrônicos. Muito há para se fazer e o tratamento via cálculos de primeiros princípios por simulações permite um caráter preditivo que corrobora na elucidação de fenômenos físicos via análises experimentais. Nesse trabalho analisamos as propriedades eletrônicas de isolantes topológicos tais como: (Bi,Sb)$_2$(Te,Se)$_3$, Germaneno e Germaneno funcionalizado. Cálculos baseados em DFT evidenciam a importância das separações entre as camadas de Van der Waals nos materiais Bi$_2$Se$_3$ e Bi$_2$Te$_3$. Mostramos que devido a falhas de empilhamento, pequenas oscilações no eixo de QLs (\\textit{Quintuple Layers}) podem gerar um desacoplamento dos cones de Dirac, além de criar estados metálicos na fase \\textit{bulk} de Bi$_2$Te$_3$. Em se tratando do Bi$_2$Se$_3$ um estudo sistemático dos efeitos de impurezas de metais de transição foi realizado. Observamos que há quebra de degenerescência do cone de Dirac se houver magnetização em quaisquer dos eixos. Além disso se a magnetização permanecer no plano, além de uma pequena quebra de degenerescência, há um deslocamento do mesmo para outro ponto da rede recíproca. No entanto, se a magnetização apontar para fora do plano a quebra ocorre no próprio ponto $\\Gamma$, porém de maneira mais intensa. Importante enfatizar que além de mapear os sítios com suas orientações magnéticas de menor energia observamos que a quebra da degenerescência está diretamente relacionada com a geometria local da impureza. Isso proporciona imagens de STM distintas para cada sítio possível, permitindo que um experimental localize cada situação no laboratório. Estudamos ainda a transição topológica na liga (Bi$_x$Sb$_{1-x}$)$_2$Se$_3$, onde identificamos um isolante trivial e topológico para $x=0$ e $x=1$. Apesar de óbvia a existência de tal transição, detalhes importantes ainda não estão esclarecidos. Concluímos que a dopagem com impurezas não magnéticas proporciona uma boa técnica para manipulação e engenharia de cone nesta família de materiais, de forma que dependendo da faixa de dopagem podemos eliminar a condutividade que advém do \\textit{bulk}. Finalmente estudamos superfícies de Germaneno e Germaneno funcionalizado com halogênios. Usando uma funcionalização assimétrica e com a avalição do invariante topológico $Z_2$ notamos que o material Ge-I-H é um isolante topológico podendo ser aplicado na elaboração de dispositivos baseados em spin. / In the search of a better understanding of the electronic and magnetic properties of topological insulators we are faced with one of its most striking features, the existence of metallic surface states with helical spin texture which are protected from non-magnetic impurities. On the surface these spin channels allows a huge potential for applications in spintronic devices. There is much to do and treating calculations via \\textit{Ab initio} simulations allows us a predictive character that corroborates the elucidation of physical phenomena through experimental analysis. In this work we analyze the electronic properties of topological insulators such as: (Bi, Sb)$_2$(Te, Se)$_3$, Germanene and functionalized Germanene. Calculations based on DFT show the importance of the separation from interlayers of Van der Waals in materials like Bi$_2$Se$_3$ and Bi$_2$Te$_3$. We show that due to stacking faults, small oscillations in the QLs axis (\\textit{Quintuple Layers}) can generate a decoupling of the Dirac cones and create metal states in the bulk phase Bi$_2$Te$_3$. Regarding the Bi$_2$Se$_3$ a systematic study of the effects of transition metal impurities was performed. We observed that there is a degeneracy lift of the Dirac cone if there is any magnetization on any axis. If the magnetization remains in plane, we observe a small shift to another reciprocal lattice point. However, if the magnetization is pointing out of the plane a lifting in energy occurs at the very $ \\Gamma $ point, but in a more intense way. It is important to emphasize that in addition to mapping the sites with their magnetic orientations of lower energy we saw that the lifting in energy is directly related to the local geometry of the impurity. This provides distinct STM images for each possible site, allowing an experimental to locate each situation in the laboratory. We also studied the topological transition in the alloy (Bi$_x$Sb$_{1-x}$)$_ 2$Se$_3$, where we identify a trivial and topological insulator for $x = 0$ and $x = 1$. Despite the obvious existence of such a transition, important details remain unclear. We conclude that doping with non-magnetic impurities provides a good technique for handling and cone engineering this family of materials so that depending on the range of doping we can eliminate conductivity channels coming from the bulk. Finally we studied a Germanene and functionalized Germanene with halogens. Using an asymmetrical functionalization and with the topological invariant $Z_2$ we noted that the Ge-I-H system is a topological insulator that could be applied in the development of spin-based devices.

Στην παρούσα Διδακτορική Διατριβή διερευνώνται αριθμητικά δομές οι οποίες μπορούν να λειτουργήσουν ως φωνονικά ή φωτονικά υλικά. Βασικό χαρακτηριστικό των φωτονικών και των φωνονικών υλικών είναι η ύπαρξη χασμάτων συχνοτήτων στη διάδοση των ηλεκτρομαγνητικών και των ελαστικών κυμάτων αντίστοιχα διαμέσου των δομών αυτών. Αρχικά διερευνήθηκαν αριθμητικά δύο δομές οι οποίες έχουν ήδη χρησιμοποιηθεί ως φωτονικά υλικά και για τις οι οποίες εξετάστηκε κατά πόσο είναι εφικτή λειτουργία τους ως φωνονικά υλικά. Η πρώτη δομή είναι η πολύ γνωστή δομή κατά στρώσεις και η δεύτερη ένας ηχητικός κυματοδηγός «λωρίδα» (slot waveguide) επάνω στον οποίο δομείται ένας φωνονικός κρύσταλλος. Για τους αριθμητικούς υπολογισμούς χρησιμοποιήθηκε η μέθοδος των πεπερασμένων διαφορών στο πεδίο του χρόνου και υπολογίστηκαν το Φάσμα Μετάδοσης καθώς και το διάγραμμα Διασποράς. Στην μελέτη αυτή περιελήφθησαν αρκετά διαφορετικά υλικά όπως το πυρίτιο, η εποξειδική ρητίνη και το βολφράμιο. Διερευνήθηκε επίσης η επίδραση όλων των γεωμετρικών παραμέτρων των δομών. Τα αποτελέσματα έδειξαν ότι οι δομές αυτές φαίνεται να έχουν πολύ ελπιδοφόρα χαρακτηριστικά ως φωνονικοί κρύσταλλοι. Υπό ορισμένες προϋποθέσεις μάλιστα μπορεί να προκύψει πλήρες τρισδιάστατο χάσμα. Λαμβάνοντας υπόψη ότι η συγκεκριμένες δομές είναι ήδη γνωστές για τη χρήση τους ως φωτονικοί κρύσταλλοι, η πεποίθηση για τη χρήση τους ταυτόχρονα ως φωτονικοί και φωνονικοί κρύσταλλοι καθίσταται βάσιμη. Στην συνέχεια, χρησιμοποιώντας ξανά τη μέθοδο των πεπερασμένων διαφορών στο πεδίο του χρόνου, μελετήθηκαν ενδεχόμενες εφαρμογές που θα μπορούσαν οι δομές αυτές να έχουν. Πιο συγκεκριμένα διερευνήθηκε αρχικά η ενδεχόμενη χρήση των φωνονικών κρυστάλλων ως αισθητήρες. Οι Ευαισθησίες αυτών των δομών υπολογίστηκαν από τις αλλαγές στα όρια των αντίστοιχων φωνονικών χασμάτων όταν ένα λεπτό φιλμ νερού (για την περίπτωση του αισθητήρα υγρασίας) προστεθεί στη δομή ή όταν οι δομές εμβαπτιστούν σε κάποιο υγρό (αισθητήρες υγρών). Μελετήθηκε επίσης για πρώτη φορά συγκεκριμένη ελαστοδυναμική συμπεριφορά της τρισδιάστατης δομής κατά στρώσεις. Τα αποτελέσματα που προέκυψαν παρουσιάζουν μια υψηλή τιμή στον λόγο της διαμήκους προς την εγκάρσια ταχύτητα του ήχου και μια ιδανική συμπεριφορά pentamode σε ένα εύρος συχνοτήτων. Τα αποτελέσματα δείχνουν σαφώς ότι η δομή κατά στρώσεις μπορεί να αποτελέσει και ένα πολύ σημαντικό ελαστοδυναμικό μεταϋλικό. Στην επόμενη ενότητα της Διδακτορικής διατριβής χρησιμοποιώντας την θεωρία συναρτησιακών πυκνότητας μελετήθηκε η φωνονική πυκνότητα καταστάσεων για υλικά τύπου γραφενίου όπως το silicene (σιλικένιο) και το germanene (γερμανένιο). Εξετάστηκαν οι περιπτώσεις στις οποίες άτομα πυριτίου ή γερμανίου στις δομές τύπου γραφενίου αντικαταστάθηκαν από άλλα άτομα της Ομάδας IV του Περιοδικού Πίνακα και διερευνήθηκε κατά πόσο οι προκύπτουσες δομές μπορούν να λειτουργήσουν ως φωνονικοί κρύσταλλοι με την εμφάνιση φωνονικών χασμάτων στην φωνονική πυκνότητα καταστάσεών τους. Εξετάστηκαν επίσης νανοσωλήνες άνθρακα και κυρίως οι ομοιότητές τους με τα υλικά τύπου γραφενίου. Βρέθηκε πως, για τις περιπτώσεις όπου η διάμετρος των νανοσωλήνων ξεπερνά το 1nm, παρουσιάζονται αρκετές ομοιότητες με τα υλικά τύπου γραφενίου. Στην τελευταία ενότητα της διατριβής διερευνώνται δομές στις οποίες μπορεί να παρατηρηθεί εντοπισμός του φωτός σε περιοχές κλίμακας νανομέτρων. Ένα σύστημα αποτελούμενο από δύο δίσκους πυριτίου με διάκενο να τους χωρίζει μερικά δέκατα του νανομέτρου μελετήθηκε πρώτο. Ο κανονικοποιημένος, αδιάστατος ενεργός όγκος καταστάσεων, V_eff, υπολογίστηκε για τους δύο χαμηλότερους συντονισμούς. Ο ενεργός όγκος καταστάσεων μειώνεται σημαντικά καθώς το χάσμα μεταξύ των δίσκων μεγαλώνει. Μελετάται επίσης μια δομή αποτελούμενη από έναν κυκλικό κυματοδηγό σχισμή ο οποίος σχηματίζεται μέσα σε έναν κυκλικό συντονιστή πυριτίου. Όπως προκύπτει από τα αριθμητικά αποτελέσματα η προτεινόμενη δομή μπορεί να εμφανίσει συντονισμούς με υψηλές τιμές του παράγοντα Q, αυξάνοντας έτσι την πεποίθηση πως η προτεινόμενη δομή μπορεί να αποτελέσει βάση για εφαρμογές σε οπτικές τηλεπικοινωνίες. / This thesis explores numerically structures that can act as phononic or photonic materials. A key feature of photonic and phononic materials is the existence of frequency gaps in propagation of electromagnetic waves and elastic waves respectively. Initially the functionality of two structures as phononic materials is numerically examined. Those structures have already been used as photonic materials. The first structure is the well-known layer-by-layer structure and the second is an acoustic strip waveguide onto which is considered one phononic crystal. For numerical calculations the Finite Difference Time Domain method was used. The transmission spectra and the band structure were calculated. Several different materials such as silicon, epoxy and tungsten were included in this study. It was also investigated the effect of all the geometric parameters of the structures. The results showed that these structures appear to have very promising features as phononic crystals. Under certain conditions it may even exists a full three-dimensional phononic band gap. Considering that those structures are already known for their use as photonic crystals, the belief for their use as both photonic crystals and phononic crystals becomes valid. Then, again using the Finite Difference Time Domain method, potential applications that these structures could have were also examined. Initially it was investigated the potential use of phononic crystals as sensors. The sensitivities of these structures were calculated from the changes in the boundaries of the respective phononic band gaps when a thin film of water (in the case of the humidity sensor) was added to the structure or when those structures immersed in a liquid (liquid sensors). Also studied for the first time the three-dimensional layer-by-layer structure for specific elastodynamic behavior. The results show a high value of the ratio of the longitudinal to the transverse speed of sound and an ideal pentamode behavior for a specific frequency range. The results clearly show that the layer-by-layer structure could be a very important elastodynamic metamaterial. In the next section of this thesis, the phonon density of states of graphene-like materials such as silicene and germanene is examined using density functional theory. Cases were silicon or germanium atoms on graphene-like structures are replaced by other group IV atoms and how these new structures could perform as nanoscale phononic crystals, creating phononic band gaps in their phonon density of states, are numerically investigated. Nanotubes were also examined and their similarities, especially for cases with diameters above 1nm, with the graphene-like materials were found. In the final section of this thesis structures which could confine light in nanometer areas were numerically examined. A system consisting of two silicon disks with in plane separation of a few tens of nanometers has been studied first. The normalized unitless effective mode volume, Veff, has been calculated for the two lowest whispering gallery modes resonances. The effective mode volume is reduced significantly as the gap between the disks decreases. It is also numerically examined a structure consisting of a circular slot waveguide which is formed into a silicon disk resonator. It is shown that the proposed structure could have high Q resonances thus raising the belief that it is a very promising candidate for optical interconnects applications.

The popularity of graphene owing to its unique properties has triggered huge interest in other two-dimensional (2D) nanomaterials. Among them, silicene shows considerable promise for electronic devices due to the expected compatibility with silicon electronics. However, the high-end potential application of silicene in electronic devices is limited owing to the lack of an energy band gap. Hence, the principal objective of this research is to tune the electronic and magnetic properties of silicene related nanomaterials through first-principles models. I first explored the impact of edge functionalization and doping on the stabilities, electronic, and magnetic properties of silicene nanoribbons (SiNRs) and revealed that the modified structures indicate remarkable spin gapless semiconductor and half-metal behaviors. In order to open and tune a band gap in silicene, SiNRs were perforated with periodic nanoholes. It was found that the band gap varies based on the nanoribbon’s width, nanohole’s repeat periodicity, and nanohole’s position due to the quantum confinement effect. To continue to take advantage of quantum confinement, I also studied the electronic and magnetic properties of hydrogenated silicene nanoflakes (SiNFs). It was discovered that half-hydrogenated SiNFs produce a large spin moment that is directly proportional to the square of the flake’s size. Next, I studied the adsorption behavior of various gas molecules on SiNRs. Based on my results, the SiNR could serve as a highly sensitive gas sensor for CO and NH3 detection and a disposable gas sensor for NO, NO2, and SO2. I also considered adsorption behavior of toxic gas molecules on boron carbide (BC3) and found that unlike graphene, BC3 has good sensitivity to the gas molecules due to the presence of active B atoms. My findings divulged the promising potential of BC3 as a highly sensitive molecular sensor for NO and NH3 detection and a catalyst for NO2 dissociation. Finally, I scrutinized the interactions of CO2 with lithium-functionalized germanene. It was discovered that although a single CO2 molecule was weakly physisorbed on pristine germanene, a significant improvement on its adsorption energy was found by utilizing Li-functionalized germanene as the adsorbent. My results suggest that Li-functionalized germanene shows promise for CO2 capture.

The main objective of this work is to research and obtain surface protected topological states in nano-ribbons created from the leaves of Germanene and Silicene. These sheets belong to the class of Topological Insulators and correspond to monolayers of germanium and silicon atoms in a hexagonal arrangement that is similar to the graphene sheet. For this investigation, we conducted a study of the electronic and structural properties of these sheets, as well as their respective nano-ribbons through first-principles calculations based on density functional theory (DFT). In this methodology we use the generalized gradient approximation (GGA) for estimating the exchange and correlation term, and the PAW method for the effective potential and the expansion of plane waves of the Kohn-Sham. We conducted a computer simulation with the aid of the package VASP (Vienna ab-initio Simulation Package). As a starting point for our research, we used the methodology of solid state physics in order to describe the crystalline structure of the leaves as well as their mutual space. Subsequently we analyze the band structure, from which many of its properties can be visualized. For this task, we initially proceeded to investigate the stability of these systems via total energy calculations, in turn obtaining the network parameters that minimizes the energy of the system. We also obtained the energy cutoff, ECUT used in our calculations, or in other words, determining the number of plane waves needed to expand the electronic wave functions on the DFT formalism. We continued our study, with the creation and analysis of two different configurations of nano-ribbons, one that corresponds to a straightforward cut of the sheet with the armchair termination pattern, and the other based on a reconstruction of those edges, which provide an energetically more stable system. Subsequently we obtained electronic structures, and conducted a study of its variation due to the change of the width of the nano-ribbon and ionic relaxation of its edges. In a way, we modified the above parameters in order to obtain a system that would give us a zero gap, or at least insignificant, as well as a specific configuration for the spin texture, in order to verify the evidence of surface protected topological states in these nano-ribbons. / O objetivo principal deste trabalho é a investigação e obtenção dos estados topologicamente protegidos de superfície em nano-fitas criadas a partir das folhas de Germaneno e Siliceno. Estas folhas pertencem a classe dos Isolantes Topológicos e correspondem a monocamadas de átomos de Germânio e Silício, em um arranjo hexagonal que se assemelha a folha do Grafeno. Para esta investigação, realizamos um estudo das propriedades eletrônicas e estruturais destas folhas, bem como de suas respectivas nano-fitas, através de cálculos de primeiros princípios fundamentados na teoria do funcional da densidade (DFT). Nesta metodologia utilizamos a aproximação do gradiente generalizado (GGA) para a estimativa do termo de troca e correlação, e o método PAW para o potencial efetivo e a expansão em ondas planas dos orbitais de Kohn-Sham. Realizamos a simulação computacional com o auxílio do pacote VASP (Vienna ab-initio Simulation Package). Como ponto de partida para nossa pesquisa, utilizamos a metodologia da física do estado sólido com o intuito de descrever a estrutura cristalina das folhas, bem como seu espaço recíproco. Posteriormente analisamos as estruturas de bandas, a partir das quais muitas de suas propriedades podem ser visualizadas. Para esta tarefa, inicialmente procedemos à investigação da estabilidade destes sistemas via cálculos de energia total, obtendo o parâmetro de rede a que minimiza a energia do sistema. Obtivemos também a energia de corte ECUT utilizada em nossos cálculos, ou em outras palavras, a determinação do número de ondas planas necessárias para expandir as funções de onda eletrônicas no formalismo da DFT. Prosseguimos nosso estudo, com a criação e análise de duas distintas configurações de nano-fitas, uma que corresponde a um corte simples e direto da folha com terminação no padrão armchair, e a outra baseada em uma reconstrução destas bordas, que acaba por fornecer um sistema mais estável energeticamente. Posteriormente obtivemos as estruturas eletrônicas, e realizamos um estudo de sua variação em função da alteração da largura da nano-fita e a relaxação iônica de suas bordas. De certa maneira, modificamos os parâmetros acima, de forma a obter um sistema que nos fornecesse um gap nulo, ou pelo menos desprezível, bem como uma determinada configuração para a textura de spin, de modo a verificarmos a evidência de uma proteção topológica nos estados de superfície nestas nano-fitas. / Mestre em Física

Na busca de um melhor entendimento das propriedades eletrônicas e magnéticas dos isolantes topológicos nos deparamos com uma das suas caraterísticas mais marcantes, a existência de estados de superfície metálicos com textura helicoidal de spin os quais são protegidos de impurezas não magnéticas. Na superfície estes canais de spin possuem um potencial enorme para aplicações em dispositivos spintrônicos. Muito há para se fazer e o tratamento via cálculos de primeiros princípios por simulações permite um caráter preditivo que corrobora na elucidação de fenômenos físicos via análises experimentais. Nesse trabalho analisamos as propriedades eletrônicas de isolantes topológicos tais como: (Bi,Sb)$_2$(Te,Se)$_3$, Germaneno e Germaneno funcionalizado. Cálculos baseados em DFT evidenciam a importância das separações entre as camadas de Van der Waals nos materiais Bi$_2$Se$_3$ e Bi$_2$Te$_3$. Mostramos que devido a falhas de empilhamento, pequenas oscilações no eixo de QLs (\\textit{Quintuple Layers}) podem gerar um desacoplamento dos cones de Dirac, além de criar estados metálicos na fase \\textit{bulk} de Bi$_2$Te$_3$. Em se tratando do Bi$_2$Se$_3$ um estudo sistemático dos efeitos de impurezas de metais de transição foi realizado. Observamos que há quebra de degenerescência do cone de Dirac se houver magnetização em quaisquer dos eixos. Além disso se a magnetização permanecer no plano, além de uma pequena quebra de degenerescência, há um deslocamento do mesmo para outro ponto da rede recíproca. No entanto, se a magnetização apontar para fora do plano a quebra ocorre no próprio ponto $\\Gamma$, porém de maneira mais intensa. Importante enfatizar que além de mapear os sítios com suas orientações magnéticas de menor energia observamos que a quebra da degenerescência está diretamente relacionada com a geometria local da impureza. Isso proporciona imagens de STM distintas para cada sítio possível, permitindo que um experimental localize cada situação no laboratório. Estudamos ainda a transição topológica na liga (Bi$_x$Sb$_{1-x}$)$_2$Se$_3$, onde identificamos um isolante trivial e topológico para $x=0$ e $x=1$. Apesar de óbvia a existência de tal transição, detalhes importantes ainda não estão esclarecidos. Concluímos que a dopagem com impurezas não magnéticas proporciona uma boa técnica para manipulação e engenharia de cone nesta família de materiais, de forma que dependendo da faixa de dopagem podemos eliminar a condutividade que advém do \\textit{bulk}. Finalmente estudamos superfícies de Germaneno e Germaneno funcionalizado com halogênios. Usando uma funcionalização assimétrica e com a avalição do invariante topológico $Z_2$ notamos que o material Ge-I-H é um isolante topológico podendo ser aplicado na elaboração de dispositivos baseados em spin. / In the search of a better understanding of the electronic and magnetic properties of topological insulators we are faced with one of its most striking features, the existence of metallic surface states with helical spin texture which are protected from non-magnetic impurities. On the surface these spin channels allows a huge potential for applications in spintronic devices. There is much to do and treating calculations via \\textit{Ab initio} simulations allows us a predictive character that corroborates the elucidation of physical phenomena through experimental analysis. In this work we analyze the electronic properties of topological insulators such as: (Bi, Sb)$_2$(Te, Se)$_3$, Germanene and functionalized Germanene. Calculations based on DFT show the importance of the separation from interlayers of Van der Waals in materials like Bi$_2$Se$_3$ and Bi$_2$Te$_3$. We show that due to stacking faults, small oscillations in the QLs axis (\\textit{Quintuple Layers}) can generate a decoupling of the Dirac cones and create metal states in the bulk phase Bi$_2$Te$_3$. Regarding the Bi$_2$Se$_3$ a systematic study of the effects of transition metal impurities was performed. We observed that there is a degeneracy lift of the Dirac cone if there is any magnetization on any axis. If the magnetization remains in plane, we observe a small shift to another reciprocal lattice point. However, if the magnetization is pointing out of the plane a lifting in energy occurs at the very $ \\Gamma $ point, but in a more intense way. It is important to emphasize that in addition to mapping the sites with their magnetic orientations of lower energy we saw that the lifting in energy is directly related to the local geometry of the impurity. This provides distinct STM images for each possible site, allowing an experimental to locate each situation in the laboratory. We also studied the topological transition in the alloy (Bi$_x$Sb$_{1-x}$)$_ 2$Se$_3$, where we identify a trivial and topological insulator for $x = 0$ and $x = 1$. Despite the obvious existence of such a transition, important details remain unclear. We conclude that doping with non-magnetic impurities provides a good technique for handling and cone engineering this family of materials so that depending on the range of doping we can eliminate conductivity channels coming from the bulk. Finally we studied a Germanene and functionalized Germanene with halogens. Using an asymmetrical functionalization and with the topological invariant $Z_2$ we noted that the Ge-I-H system is a topological insulator that could be applied in the development of spin-based devices.