Excitons in intrinsic and bilayer graphene

Through first-principles calculations with many-body effects included, we have revealed unique excitonic effects in the high-frequency regime ($10~20$ eV) of optical spectra of graphene and bilayer graphene (BLG). Despite their different symmetries, the parallel $\sigma$ and ${\pi }^{*}$ bands result in enhanced excitonic effects in such two-dimensional (2-D) semimetals; one narrowly resonant exciton is discovered to form an isolated peak below the prominent absorption continuum with a surprisingly large binding energy; 270 meV in graphene and 80 meV in BLG. Moreover, because of its extremely weak resonant character, this exciton displays a bound electron-hole wave function and possesses a long intrinsic lifetime, which might be useful in designing optoelectronic applications of graphene.

Figure 1

Quasiparticle band structure of graphene. Dashed oval circled bands are nearly free electronic states. The Fermi level is set to be zero.

Figure 2

Optical absorption spectra with and without e-h interaction included, respectively. Panel (a) shows graphene and (b) shows BLG. The absorbance can be directly compared to experimental measurements.[11] The absorption continuum edge between $\sigma$ and ${\pi }^{*}$ bands is marked by a black arrow in (a). The absorbance below 0.3 eV is not shown because no Drude factor is included. A 0.08-eV Gaussian broadening is applied.

Figure 3

$S_i(\omega )$ and the corresponding integration $I(\omega )={\int }_0^{\omega }{S}_i({\omega }^{\prime })\hspace{0.5em}d{\omega }^{\prime }$ of two optically bright states in graphene from GW-BSE calculations. Their eigenenergy is marked by dashed cyan lines as well.

Figure 4

Exciton charge distributions of the two bright exciton states depicted in Fig. 3 for graphene. The electron amplitude squared is plotted, given that the hole is fixed at the black spot. The distributions have been averaged along the direction perpendicular to the graphene plane.

Figure 5

Exciton charge distributions of two bright exciton states in BLG, respectively, with the hole fixed at the black spot. The one plotted in (a) and (c) is the nearly bound exciton located at 12.7 eV and the one plotted in (b) is a resonant exciton located at 14.8 eV. (a) and (b) are the top view and (c) is the side view. These distributions are integrated along the view direction, respectively.