In this thesis, I present a theory of electron-electron interactions in optical properties of graphene and transition metal dichalcogenides (TMDCs), two dimensional nanostructures with a hexagonal lattice. We start our discussion with electron-electron interactions in artificial rings for which the strength of interactions can be varied and exact results can be obtained. The artificial rings are described by the extended Hubbard model and solved using an exact diagonalization method in real and Fourier space of configurations. Exact and analytical results for charged rings are obtained in the limit of very strong interactions. For the quadruple quantum dot ring and the artificial benzene ring, we find that chirality leads to the appearance of a topological phase and an effective gauge field that determines the ground state character with varied interaction strength. For the charged artificial benzene ring, our numerical results show a transition from a degenerate to a non-degenerate ground state with increasing strength of Coulomb interactions. We show that the artificial gauge and the transition in the ground state can be detected as changes in the optical absorption spectrum. In the second part of the thesis, the electronic and optical properties of colloidal graphene quantum dots (CGQD) consisting of many benzene rings are determined. The CGQDs are described by the combination of tight binding, mean field Hartree Fock (HF) and Configuration Interaction methods. The single particle properties are described through the tight binding method based on the pz carbon orbitals. Screened Coulomb interactions between electrons, including direct, exchange, and scattering matrix elements, are calculated using Slater pz orbitals. HF ground states corresponding to semiconductor, Mott-insulator, and spin-polarized phases are obtained as a function of the strength of the screened interaction versus the tunnelling matrix element. The many-body ground and excited states in the semiconducting phase are constructed as a linear combination of a finite number of electron-hole pair excitations from the HF ground state (GS). The Hamiltonian is constructed in the subspace of multi-pair HF excitations to obtain the low energy, many body states by exact diagonalization using the Lanczos method. The degeneracy of the valence- and conduction-band edges of 3-fold rotationally symmetric CGQDs is shown to lead to a characteristic exciton and bi-exciton spectrum. The low-energy exciton spectrum is predicted to consist of two bright-singlet exciton states corresponding to two circular polarizations of light and a lower-energy band of dark singlets and dark triplets. The robustness of the bright degenerate singlet pair against correlations in the many-body state is demonstrated as well as the breaking of the degeneracy by the lowering of symmetry of the CGQD. Band edge biexciton energies and binding energies are predicted, and two degenerate exciton (X) states and a corresponding biexciton (XX) state are identified for the generation of an XX-X cascade. The Auger coupling of XX and excited X states is determined and our theoretical results are compared with experimental absorption and non-linear transient absorption spectra. In the third and final part of the thesis, we replace the two non-equivalent carbon atoms of the graphene hexagonal lattice with a heavy transition-metal atom M, (e.g. Mo or W) and a dimer X2 (e.g. S). The bandstructure of a monolayer MX2 is calculated using density functional theory (DFT). It is shown that a direct gap opens up at all K points of the Brillouin zone and strong spin orbit coupling leads to spin splitting of the valence and conduction bands and emergence of valley dependent optical selection rules. Finally, the magnetoluminescence experiments on a monolayer WS2 emitting circularly polarized light upon its excitation by unpolarized light are described. The emission of polarized light in zero magnetic field is explained by the possibility of formation of a valley polarized 2D electron gas in unintentionally doped WS2.

[pt] s pontos quânticos de grafeno têm potencial para aplicações biológicas devido às suas propriedades ópticas e de tamanho nanométrico. Este estudo investigou por 28 dias (672 h) as interações de GQDs de diferentes precursores (ácido cítrico + ureia e ácido cítrico + tioacetamida) com biomoléculas modelo (albumina sérica humana - HSA) e DNA do timo de bezerro (ctDNA). Os GQDs-ureia mostraram estabilidade no diâmetro hidrodinâmico (12 nm) e carga superficial (-7 mV). Já os GQDs-tioacetamida apresentaram agregação progressiva de 5,0 nm iniciais para 22,7 nm após 28 dias, sem sedimentação devido à compensação de cargas preservando a dispersão coloidal. Ensaios revelaram supressão da fluorescência da HSA com aumentos na concentração dos GQDs. A constante de interação (Ki) GQDs-ureia oscilou inicialmente, estabilizando após 48 h. Para GQDs-tioacetamida houve menor flutuação de Ki ao longo de 672 h, indicando rearranjos conformacionais das biomoléculas com os GQDs antes do equilíbrio. A interação com o DNA, acompanhada por titulação absorciométrica no UV-Vis mostrou biointeração fraca de natureza hidrofóbica/eletrostática para ambos GQDs, com constantes de ligação aparentes (∼105 L mol−1). Ensaio com brometo de etídio revelou alterações na estrutura do DNA sem intercalação dos GQDs.Testes estatísticos confirmam a reprodutibilidade das interações dos GQDs com proteínas (HSA) e DNA no período de 28 dias (95 por cento de confiança). A estabilidade dos parâmetros de quantificação ao longo do tempo sugere a viabilidade dos GQDs como sondas analíticas após longos períodos de bioconjugação. Assim, o estudo apresenta bases metrologicamente sólidas para aplicação segura de GQDs em tecnologias biomédicas, expandindo o entendimento da relação tempo-estrutura-atividade nesses nanossistemas. / [en] Graphene quantum dots have potential for biological applications due to their optical properties and nanometric size. This study investigated for 28 days (672 h) the interactions of GQDs from different precursors (citric acid + urea and citric acid + thioacetamide) with model biomolecules (human serum albumin - HSA) and Calf thymus DNA (ctDNA). The GQDs-urea showed stability in hydrodynamic diameter (12 nm) and surface charge (- 7 mV). In contrast, GQDs-thioacetamide showed progressive aggregation from 5.0 nm initially to 22.7 nm after 28 days, without sedimentation due to charge compensation preserving colloidal dispersion. Tests revealed quenching of HSA fluorescence with increases in GQD concentration. The GQDs-urea interaction constant (Ki) fluctuated initially, stabilizing after 48 h. For GQDs-thioacetamide there was less fluctuation in Ki over 672 h, indicating conformational rearrangements of the biomolecules with the GQDs before equilibrium. Interaction with DNA monitored by UV-Vis photometric absorption titration showed weak bio-interaction of a hydrophobic/electrostatic nature for both GQDs, with apparent binding constants (∼105 L mol−1). Ethidium bromide assay revealed changes in DNA structure without intercalation of the GQDs. Statistical tests confirm the reproducibility of GQDs interactions with proteins (HSA) and DNA over 28 days (95 percent confidence). The stability of the quantification parameters over time suggests the viability of GQDs as analytical probes after long periods of bioconjugation. Thus, the study presents metrologically sound bases for the safe application of GQDs in biomedical technologies, expanding the understanding of the time-structure-activity relationship in these nanosystems.

[pt] Uma sonda fotoluminescente do tipo turn-on foi avaliada para a detecção de putrescina usando pontos quânticos de grafeno (GQDs). Diferentes nanopartículas de carbono fotoluminescentes foram preparadas usando a abordagem bottom-up, usando ácido cítrico como precursor, sozinho ou misturado com outros compostos contendo heteroátomos (N e/ou S) visando funcionalização da nanoestrutura. Observou- se que as nanopartículas preparadas com ácido cítrico e tioureia (GQDs-TU) apresentaram melhor perfil aumento da fotoluminescência (resposta analítica) na presença dessa amina biogênica. As condições experimentais foram ajustadas para o melhor perfil de resposta e para obter os parâmetros analíticos de mérito. No ensaio em batelada, a curva analítica normalizada (concentração L-L0 versus PUT) foi linear (R2 = 0,9498) até 90 mg L1 . O limite de quantificação (LOQ) foi de 15,1 mg L-1 e o limite de detecção (LOD) foi de 4,5 mg L-1 . Além disso, a estratégia proposta para a determinação indireta de putrescina foi adaptada para um sistema de análise por injeção em fluxo (FIA) a fim de aumentar a frequência analítica, diminuir os resíduos e automatizar a quantificação do analito. Após a otimização do ensaio, com a faixa linear cobrindo o intervalo até 50 mg L-1 (R2 = 0,9980), os valores de LOD e LOQ foram 3,0 mg L1 e 9,9 mg L-1 , respectivamente. / [en] A photoluminescent turn-on probe was evaluated for putrescine detection using graphene quantum dots (GQDs). Different photoluminescent carbon nanoparticles were prepared using a bottom-up approach, employing citric acid as a precursor, either alone or mixed with other compounds containing heteroatoms (N and/or S) for nanostructure functionalization. It was observed that the nanoparticles prepared with citric acid and thiourea (GQDs-TU) exhibited a more pronounced increase in photoluminescence (analytical response) when exposed to this biogenic amine. Experimental conditions were fine-tuned to optimize the response profile and obtain the analytical parameters of merit. In the batch assay, the normalized analytical curve (L-L0 concentration versus PUT) was linear (R2 = 0,9498) up to 90 mg L-1 . The limit of quantification (LOQ) was 15,1 mg L-1 and the limit of detection (LOD) was 4,5 g L-1 . Furthermore, the proposed strategy for the indirect determination of putrescine was adapted for a flow injection analysis (FIA) system to increase the analytical frequency, reduce waste, and automate analyte quantification. After optimization of the assay, with the linear range covering the range up to 50 mg L-1 (R2 = 0,9980), the LOD and LOQ values were 3,0 mg L-1 e 9,93 mg L-1 , respectively.