Theoretical study on electronic properties of curved graphene quantum dots

Electronic properties of curved graphene quantum dots (CGQDs) were studied using Density Functional Theory (DFT) method. Two shapes of the zigzag-edged CGQDs, i.e., rhomboidal (RGQDs) and hexagonal (HGQDs) graphene quantum dots, and each with five sizes were studied. For each GQD, its structure was curved along symmetry-unique folding axes at 2(0), 4(0), 6(0), 8(0), 10(0), 12(0), 14(0), and 16(0). There are four unique folding axes (FA1, FA2, FA3, and FA4) for RGQDS and only two axes for HGQDs (FA1 and FA2). The results showed that HOMO and LUMO energies of CGQDs depend on size, shape, folding axis, and folding degree. The band gap (HOMO-LUMO gap) at different folding degrees were monitored for all structures. For the folding at FA1, FA2, and FA4 of RGQDs and FA1 and FA2 of HGQDs, the narrowing of the band gap was observed, while only for the folding at FA3 of RGQDs the band gap widening was found. Orbital interactions can explain the narrowing/widening of the band gap of CGQDs. The energy used for curving GQDs (the deformation energy) depends on the size and folding axis but not their shape. The "armchair-like" folding has higher deformation energy than the "zigzag-like" one. The deformation energy is related to the folding strain and the number of the same-symmetry axis. The number of the same-symmetry axis is also related to the size of GQDs.