Analytical study of electronic structure in armchair graphene nanoribbons

Abstract

We present the analytical solution of the wavefunction and energy dispersion of armchair graphene nanoribbons (GNRs) based on the tight-binding approximation. By imposing hard-wall boundary condition, we find that the wavevector in the confined direction is discretized. This discrete wavevector serves as the index of different subbands. Our analytical solutions of wavefunction and associated energy dispersion reproduce the numerical tight-binding results and the solutions based on the k · p approximation. In addition, we also find that all armchair GNRs with edge deformation have energy gaps, which agrees with recently reported first-principles calculations.

Electrical Properties of Graphene for Interconnect Applications

“…As a conclusion, in the case of a long wavelength limit, the conductivity of graphene does not show spatial dispersion, but only frequency dispersion, according to Equation (22). For a GNR (as in Figure 3), the conductivity may be assumed to have only the longitudinal component σ xx (ω,0) = σ(ω).…”

“…Given the number N and, thus, the GNR width, w, the energy spectrum of the π-electrons can be obtained by slicing the band structure of graphene in Figure 2 (e.g., [20,22,23]). Figure 4 shows the band structure for an armchair GNR, assuming N = 5 and N = 6.…”

Nonlinear transverse current response in zigzag graphene nanoribbons

“…GNRs exhibit physical properties distinct from those of infinite graphene sheets. [14][15][16][17][18][19] While the optical response of graphene is in the order of the universal conductance with the absorption around a few per cent in the far infrared and visible range, [22][23][24][25] the response in graphene structures with reduced dimensionality, such as ribbons, can be significantly stronger. 20,21 In this paper, we employ a self-consistent approach to reveal some unique electronic properties in ZGNRs subject to a crossed electric and magnetic field.…”

Terahertz transitions in carbon nanotubes and graphene nanoribbons

“…We show that this equivalence extends to optical transitions selection rules. The aforementioned edge effect in armchair ribbons can be again incorporated into the tight-binding model as small corrections to the hopping integrals [19]. Our calculations, presented in Fig.…”