Quantum size effects in the atomistic structure of armchair nanoribbons

Abstract

Quantum size effects in armchair graphene nano-ribbons (AGNR) with hydrogen termination are investigated via density functional theory (DFT) in Kohn-Sham formulation. "Selection rules" will be formulated, that allow to extract (approximately) the electronic structure of the AGNR bands starting from the four graphene dispersion sheets. In analogy with the case of carbon nanotubes, a threefold periodicity of the excitation gap with the ribbon width (N , number of carbon atoms per carbon slice) is predicted that is confirmed by ab initio results. While traditionally such a periodicity would be observed in electronic response experiments, the DFT analysis presented here shows that it can also be seen in the ribbon geometry: the length of a ribbon with L slices approaches the limiting value for a very large width 1 ≪ N (keeping the aspect ratio small N ≪ L) with 1/Noscillations that display the electronic selection rules. The oscillation amplitude is so strong, that the asymptotic behavior is non-monotonous, i.e., wider ribbons exhibit a stronger elongation than more narrow ones.

Ab initioquantum transport through armchair graphene nanoribbons: Streamlines in the current density

“…counts the energy bands intersecting with a given energy E. The bandgap characteristic of all AGNRs with its three-fold periodicity is clearly seen -minimum with AGNRs(3m−1), m∈N (≈0.1 eV). This observation reflects a well-known behaviour [24][25][26][27]39 . The corresponding current densities dj(r)/dV bias are shown in Fig.…”

“…This strong interest in GNRs is closely related to their electronic properties: GNRs exhibit a bandgap [24][25][26] that can be tuned with the ribbon width. This makes them promising materials for applications, e.g., in organic optoelectronics.…”

Current density and conductivity through modified gravity in the graphene with defects

“…During the last years, graphene has been in the focus of frontier research, since its mass energy excitation for fermions is low, as it emerges from the symmetries of the honeycomb lattice [1][2][3][4][5][6][7]9]. This research has led to many important results.…”

Incommensurate quantum-size oscillations in acene-based molecular wires—Effects of quantum fluctuations

“…1). The procedure is analogous to the threefold periodicity in band-gaps of nanotubes 13 and nanoribbons; 14,15 in the acene case, however, incommensurate periodicity is reached because of the FIG. 1.…”

“…An established example is given by the threefold gaposcillation of zigzag carbon nanotubes (armchair-ribbons) as a function of tube diameter (width). [13][14][15] In this context, the three-fold periodicity reflects the symmetry of the hexagonal Brillouin zone, with the Dirac points located at the corners. A remarkable aspect of the acene oscillations is that they are incommensurate in the sense that the oscillation period is not dictated by lattice symmetry; it can reach periods of ten times the length of the unit cell.…”