Optical properties of graphene nanoribbons: The role of many-body effects

We investigate from first principles the optoelectronic properties of nanometer-sized armchair graphene nanoribbons (GNRs). We show that many-body effects are essential to correctly describe both energy gaps and optical response. As a signature of the confined geometry, we observe strongly bound excitons dominating the optical spectra, with a clear family-dependent binding energy. Our results demonstrate that GNRs constitute one-dimensional nanostructures whose absorption and luminescence performance can be controlled by changing both family and edge termination.

Figure 1

(a) Optical absorption spectra of 1-nm-wide hydrogen-passivated GNRs: $N=8$ ($1.05\mathrm{nm}$ wide), 9 $\left(1.17\mathrm{nm}\right)$, and 10 $\left(1.29\mathrm{nm}\right)$. In each panel, the solid line represents the spectrum with electron-hole interaction, while the spectrum in the single-particle picture is in gray. All the spectra are computed introducing a Lorentzian broadening. (b) Quasiparticle band structures.

Figure 2

(Color online) In-plane spatial distribution of the electron for a fixed hole position (black dot), corresponding to the lowest excitonic peak in the $N=9$ case. The spatial density is averaged over the direction orthogonal to the ribbon plane. Dimension of the panel: $1.2\times 6.4{\mathrm{nm}}^2$.

Figure 3

(Color online) (a) Quasiparticle band structure of the $N=9$ hydrogen-free GNR. Arrows indicate the edge-related single-particle bands. (b) Plot of $GW$ quasiparticle energies vs LDA energies for different states and $k$ points. (c) Optical absorption spectrum, with (black) and without (gray) excitonic effects. The black arrow indicates the position of the dark edge-related exciton. Its excitonic wave function is depicted in (d), whose dimension is $1.0\times 2.2{\mathrm{nm}}^2$.