Excitonic Effects in the Optical Conductivity of Gated Graphene

We study the effect of electron-electron interactions in the optical conductivity of graphene under an applied gate and derive a generalization of Elliott’s formula, commonly used for semiconductors, for the optical intensity. We show that excitonic resonances are responsible for several features of the experimentally measured midinfrared response of graphene such as the increase of the conductivity beyond the universal value above the Fermi blocked regime, the broadening of the absorption at the threshold, and the decrease of the optical conductivity at higher frequencies.

Figure 1

Real and imaginary parts of the conductivity. The black dashed line is obtained from the independent electron model with disorder. The solid red line is the model given in the text, which includes excitonic corrections and disorder. The experimental curves, refer to a gate voltage of 28 V, to which corresponds a Fermi energy of $\mu \simeq 0.18\mathrm{eV}$. In the experiment 14, the chemical potential was given by $\mu =0.03474\sqrt{V}g\mathrm{eV}$. The calculation took an effective temperature of 120 K [see the discussion in point (ii) in the text]. In the left inset we give the transmission, $T$, of neutral graphene, as a function of $\hslash \omega$, in comparison with the experimental data of Ref. 12. In the right inset we show the dc conductivity as a function of gate voltage, comparing both the experimental data (blue line) of Ref. 14 and the theoretical fit; the fit fixes the concentration of impurities, to the values of $n_i=2\times {10}^{11}{\mathrm{cm}}^{-2}$, for resonant scatterers, and $n_i=1\times {10}^{11}{\mathrm{cm}}^{-2}$, for charged ones. The determined impurity concentrations are then used in the calculation of the optical conductivity. Therefore, the calculation of the optical conductivity has no fitting parameter. The labels (i), (ii), (iii), (iv), and (v), refer to the five items discussed in the text.