Comment on “Orientation dependence of the optical spectra in graphene at high frequencies”

Zhang et al. [Phys. Rev. B 77, 241402(R) (2008)] reported a theoretical study of the optical spectra of monolayer graphene employing the Kubo formula within a tight-binding model. Their calculations predicted that at high frequencies the optical conductivity of graphene becomes strongly anisotropic. In particular, at frequencies comparable to the energy separation of the upper and lower bands at the $\mathrm{\Gamma }$ point, the optical conductivity is strongly suppressed if the field polarization is along the zigzag direction whereas it is significantly high for the armchair one. We find that, unfortunately, this result is just a consequence of the incorrect determination of the current operator in $k$ space. Here, we present a standard scheme to obtain this operator correctly. As a result, we show that the optical conductivity of monolayer graphene is indeed isotropic, which is consistent with the results of other (both theoretical and experimental) studies in the literature.

Figure 1

Schematic of a graphene lattice with the conventions for vectors ${\mathbf{t}}_{1,2}$ and ${\mathbf{\delta }}_{1–3}$ used in the text.

Figure 2

Corrected optical conductivity in comparison with the calculations of Zhang et al. in Ref. [4] (${\sigma }_0=e^2/4\hslash$).

Figure 3

(a) Incorrect unit-cell dependence of optical conductivity obtained using the scheme as in Refs. [3, 4], in comparison with (b) the correct ones obtained using the scheme presented in this Comment (${\sigma }_0=e^2/4\hslash$).