Optical conductivity of hydrogenated graphene from first principles

We investigate the effect of hydrogen coverage on the optical conductivity of single-side hydrogenated graphene from first-principles calculations. To account for different degrees of uniform hydrogen coverage we calculate the complex optical conductivity for graphene supercells of various sizes, each containing a single additional hydrogen atom. We use the linearized augmented plane wave method, as implemented in the wien2k density functional theory code, to show that the hydrogen coverage strongly influences the complex optical conductivity and thus the optical properties, such as absorption, of hydrogenated graphene. We find that the optical conductivity of graphene in the infrared, visible, and ultraviolet range has different characteristic features depending on the degree of hydrogen coverage. This opens up new possibilities to tailor the optical properties of graphene by reversible hydrogenation, and to determine the hydrogen coverage of hydrogenated graphene samples in the experiment by contact-free optical absorption measurements.

Figure 1

Comparison of different systems investigated in this study using quantum espresso structure optimization data. The unit cell of graphone (a) contains 2 C + 1 H atoms and has a single-side hydrogen coverage of $50\%$. The larger $2\times 2$ (b) and $5\times 5$ (c) supercells contain 8 C + 1 H and 50 C + 1 H atoms, respectively, accounting for $12.5\%$ and $2\%$ of hydrogen coverage. Pure graphene (d) with two C atoms per unit cell corresponds to $0\%$ hydrogen coverage. The lattice constant $a$ is given for each system.

Figure 2

Calculated electronic band structure along high-symmetry lines in the first Brillouin zone (left panels) and broadened total DOS per unit cell (right panels) for the nonmagnetic (a) and the spin-polarized (b) $50\%$ SSH case (graphone). In the spin-polarized case the spin-resolved total DOS is shown; quantities associated with spin up (down) are shown as solid red (dashed blue) lines. Energies are given relative to the Fermi energy $E_F$. Labeled arrows indicate direct interband transitions corresponding to pronounced features in the optical conductivity spectra (see Fig. 6).

Figure 3

See the caption of Fig. 2, but for the $12.5\%$ SSH case ($2\times 2$ supercell).

Figure 4

See the caption of Fig. 2, but for the $2\%$ SSH case ($5\times 5$ supercell).

Figure 5

See the caption of Fig. 2, but for nonmagnetic pure graphene.

Figure 6

Calculated real part of the complex optical conductivity $\sigma$ for $50\%$ (a), $12.5\%$ (b), and $2\%$ (c) SSH graphene, as well as pure graphene (d), given in units of the universal ac optical conductivity ${\sigma }_0$ of graphene. Pronounced features of the spectra are labeled in concordance with the arrows in Figs. 2, 3, 4, 5, indicating the most important transitions contributing to them.

Figure 7

Calculated real part of the complex optical conductivity $\sigma$ in units of the universal ac optical conductivity ${\sigma }_0$ of graphene for $50\%$ SSH graphene, comparing the nonmagnetic, the spin-polarized, and another spin-polarized but unrelaxed flat case, in which all carbon atoms are restricted to the same plane.