We numerically investigate quantum rings in graphene and find that their electronic properties may be strongly influenced by the geometry, the edge symmetries, and the structure of the corners. Energy spectra are calculated for different geometries (triangular, hexagonal, and rhombus-shaped graphene rings) and edge terminations (zigzag, armchair, as well as the disordered edge of a round geometry). The states localized at the inner edges of the graphene rings describe different evolution as a function of magnetic field when compared to those localized at the outer edges. We show that these different evolutions are the reason for the formation of subbands of edge-states energy levels, separated by gaps (anticrossings). It is evident from mapping the charge densities that the anticrossings occur due to the coupling between inner and outer edge states.

Black phosphorus has recently emerged as a new layered crystal that, due to its peculiar and anisotropic crystalline and electronic band structures, may have important applications in electronics, optoelectronics and photonics. Despite the fact that the edges of layered crystals host a range of singular properties whose characterization and exploitation are of utmost importance for device development, the edges of black phosphorus remain poorly characterized. In this work, the atomic structure and behaviour of phonons near different black phosphorus edges are experimentally and theoretically studied using Raman spectroscopy and density functional theory calculations. Polarized Raman results show the appearance of new modes at the edges of the sample, and their spectra depend on the atomic structure of the edges (zigzag or armchair). Theoretical simulations confirm that the new modes are due to edge phonon states that are forbidden in the bulk, and originated from the lattice termination rearrangements.

The electronic and transport properties of an extended linear defect embedded in a zigzag nanoribbon of realistic width are studied within a tight-binding model approach. Our results suggest that such a defect profoundly modifies the properties of the nanoribbon, introducing new conductance quantization values and modifying the conductance quantization thresholds. The linear defect along the nanoribbon behaves as an effective third edge of the system, which shows a metallic behavior, giving rise to new conduction pathways that could be used in nanoscale circuitry as a quantum wire. DOI: http://dx.doi.org/10.1103/PhysRevB.83.155436 ©2011 American Physical Society

Using a combined molecular dynamics – tight-binding simulation scheme we access the electronic transport signatures of graphene with embedded nanobubbles.