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Spin-resolved band structure and spin density plots for single substitutions in (a) h-BN and (b) graphene. Left and right panels of bandstructure correspond to the spin-up and spin-down bands, respectively. The dotted lines represent bulk graphene bands and the horizontal dashed line marks the Fermi level.
Impurity state levels and trends of energy difference between S = 0 and S = 1 spin-state for 2-D h-BN with carbon substitutions. (a) and (b) two C atoms are at A-B sublattice sites-substituting a B and a N atom. (c) and (d) both C atoms are substituting B (or N) atoms, the A-A interaction. In both cases, there are four energy spectrum panels and the exchange trend as a function of separations. Each spectrum panel is divided by a dashed line into two, representing states for each of two C atoms. If both C atoms contribute equally to the formation of states, the states are drawn across the dashed line and the center of the line segment being at the dashed line.
Changes in formation energy with increasing separation of a B (C) atom from the position of a B-N pair (C-C pair) or a B-N (C) hexagonal-ring embedded in graphene (h-BN). The energy of a pair or the closed hexagonal ring configuration is set to be zero. We refer to the position change of the B (C) atom marked by a cross from the pair configuration to one of sites labeled by triangles or squares as the “zigzag” or “armchair” separation, respectively. For hexagonal-rings, only “armchair” separations are studied and sites are labeled by diamonds. Filled and open symbols correspond to two inequivalent sublattice sites of the 2D hexagonal lattice.
Energy spectra for graphene quantum dots embedded in h-BN. (a)-(i) present gradually changing spectra of a 10 × 10 supercell of h-BN containing up to nine C hexagonal rings, whereas (j)-(l) pertain to the six-fold symmetric hexagonal ring configurations containing one, seven, and nineteen rings. The energies for (a)-(b) structures lie in the UV range, those for (c)-(g) span the visible spectrum, whereas (h)-(i) belong to the infrared region. For the six-fold symmetric configurations, the structure (j) lies within the UV range, whereas the configurations (k)-(l) are both contained within the visible range of the electromagnetic spectrum.
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