We present results of tight binding calculations demonstrating existence of degenerate electronic shells of Dirac fermions in narrow, charge neutral graphene quantum rings. We predict removal of degeneracy with finite magnetic field. We show, using a combination of tight binding and configuration interaction methods, that by filling a graphene ring with additional electrons this carbon based structure with half-filled shell acquires a finite magnetic moment.
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Optical properties of transition metal dichalcogenides monolayer of MoS₂ are analyzed using multi-orbital tight-binding models with only Mo d-orbitals (three-band model) and with an inclusion of S p-orbitals (six-band model). We look at band structures, momentum matrix elements between valence and conduction band, and joint optical density of states. Good agreement between the two models is shown in a vicinity of K point of the Brillouin zone. On line connecting K and Γp points, a local conduction band minimum at Q point is recovered only by six-band model in agreement with density functional theory and experimental results. We show that optical transitions at this point are active for both light polarizations. A peak in joint optical density of states is also seen at this point suggesting its potentially important role in a proper description of excitonic effects.
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