Theoretical study of optical conductivity of graphene with magnetic and nonmagnetic adatoms

We present a theoretical study of the optical conductivity of graphene with magnetic and nonmagnetic adatoms. First, by introducing an alternating potential in a pure graphene, we demonstrate a gap formation in the density of states and the corresponding optical conductivity. We highlight the distinction between such a gap formation and the so-called Pauli blocking effect. Next, we apply this idea to graphene with adatoms by introducing magnetic interactions between the carrier spins and the spins of the adatoms. Exploring various possible ground-state spin configurations of the adatoms, we find that the antiferromagnetic configuration yields the lowest total electronic energy and is the only configuration that forms a gap. Furthermore, we analyze four different circumstances leading to similar gaplike structures and propose a means to interpret the magneticity and the possible orderings of the adatoms on graphene solely from the optical conductivity data. We apply this analysis to the recently reported experimental data of oxygenated graphene.

Figure 1

Illustration of graphene in the presence of adatoms. The honeycomb net represents a graphene lattice. The black filled and opaque circles represent adatoms sitting at sublattices $A$ and $B$, respectively. Parallelograms with different colors and line styles represent supercells with different configurations of adatom occupation: black-solid lines (dotted-red lines) for a supercell containing only an adatom at sublattice $A\left(B\right)$, dashed-green lines for a supercell containing adatoms at both sublattices, and dot-dashed-blue lines for a supercell with no adatoms.

Figure 2

Comparison between optical conductivity of (a) bare graphene, (b) graphene with an alternating potential, and (c) charged graphene. The magnitudes of the alternating potential and the chemical potential are taken to be as follows: $V=\mu =0$ for the bare graphene, $V=0.5\mathrm{eV},\mu =0$ for graphene with an alternating potential, and $V=0,\mu =0.5\mathrm{eV}$ for charged graphene, respectively. The insets show the DOS for the three cases where the small vertical arrowed line in each inset indicates the position of the chemical potential.

Figure 3

Comparison of optical conductivities of graphene with 100% adatom coverage for various possible magnetic configurations. The main panel shows the optical conductivity for (a) AFM, (b) FM, and (c) PM ground states, respectively. The insets show their corresponding DOS profiles.

Figure 4

Comparison of ${\sigma }_1\left(\omega \right)$ between experimental data and calculation results. (a) The experimental data of oxygenated graphene for various times of oxygen exposure (replotted from Ref. [10]). (b) and (c) Graphene systems with FM- and AFM-ordered adatoms, respectively, for various adatom concentrations $\left(x\right)$. (d) Graphene with nonmagnetic adatoms for various chemical potential values $\left(\mu \right)$. (e) Graphene with magnetic adatoms of the PM configuration with $\mu$ increasing proportionally to $x$. The vertical red dashed line is to mark the energy value below which the experimental data are not available for comparison.