Quasiparticle energy and optical excitations of gated bilayer graphene

By employing the first-principles $GW$-Bethe-Salpeter equation simulation, we obtain the accurate quasiparticle (QP) band gap and optical absorption spectra of gated bilayer graphene. Enhanced electron-electron interactions dramatically enlarge the QP band gap; infrared optical absorption spectra are dictated by bright bound excitons. In particular, the energies of these excited states can be tuned in a substantially wider range, by the gate field, than previous predictions. Our results clearly explain recent experiments and satisfactorily resolve the inconsistency between experimentally measured transport and optical band gaps. Moreover, we predict that the most deeply bound exciton is a dark exciton which is qualitatively different from the hydrogenic model, and its electron and hole are condensed onto opposite graphene layers, respectively. This unique dark exciton not only impacts the exciton dynamics but also provides an exciting opportunity to study entangling exchange effects of many-body physics.

Figure 1

(a) DFT/LDA and $GW$ calculated band structures around the Dirac point of BLG under a gate field of 2 V/nm. (b) Comparison of the “gap” values obtained from different approaches and their dependence on the gate electric field. The value of the optical gap is defined by the position of the first bright peak of the optical absorption spectrum. Experimental values are extracted from Ref. 9.

Figure 2

(a) Optical absorption spectra of GBLG. The vertical dash-dotted (black) line indicates the $GW$ fundamental gap. The incident light is polarized parallel to the graphene plane. A 10-meV Gaussian smearing is applied. (b) Optical activity and eigenenergy of excitons. Each bar represents one exciton state and its height (plotted on a logarithmic scale) indicates the corresponding optical activity. The lowest-energy dark exciton D and the prominent exciton A are outlined by wide black and red bars, respectively.

Figure 3

(a) Distribution of the single-particle oscillator strength in the reciprocal space. We only include transitions from the highest valence band to the lowest conduction band. (b), (c) Distributions of the square of the exciton amplitude ($|A_{vc\mathbf{k}}^S{|}^2$) of the dark exciton D and bright exciton A in the reciprocal space. The filled (black) squares mark the three identical locations of the minimum energy gap.

Figure 4

(a), (b) Side views of an isosurface plot of the square of wave functions of excitons D and A. (c)–(f) Top view of these exciton wave functions for the top and bottom layers, respectively. The hole position is marked by the open circle in (a) and (b), while it is located at the center of the bottom layer in (d) and (f).