Crossover in the adsorption properties of alkali metals on graphene

The adsorption of alkali metals (AMs) on single layer graphene is studied using first principles methods. We observe a common trend in the binding distance, the charge transfer, and the work function $\left(W\right)$ at certain coverage of AMs with increase in the proportion $\rho$ (adatom/C atom) of the graphene covered by the AM. A dip in these properties occurs at $\rho \approx 0.04$ for all AMs except Li, for which it occurs at $\rho \approx 0.08$. This behavior is due to a transition of adsorbed metals from individual atoms to two-dimensional metallic sheets that exert a depolarization effect. $W$ of graphene exhibits asymmetric dependence on $\rho$: a dip in the adatom layer side but saturation on the graphene side, which is in contrast to the case of bulk graphite.

Figure 1

(Color online) Schematic atomic structure of alkali metal-adsorbed graphene. Adatoms in hollow sites on graphene in (a) $2\times 2$ and (b) $4\times 4$ supercell structure. Green (large gray) circles: alkali metal atoms; yellow (small gray) circles: carbon atoms; red parallelograms: unit cells.

Figure 2

(Color online) (a) Calculated binding energy $E_{ad}$ of AMs on graphene at varying adatom coverages ($\rho$, adatom/C) and (b) charge transfer from adatom to graphene per adatom ($n_{ad}$, filled data points) or per carbon atom ($n_c$, open data points). The curves of $1/\rho$ for $n_{ad}$ in (b) are the analytic form obtained by minimizing the adsorption energy with respect to the coverage (see the text). For Li, the trends of $E_{ad}$ and charge transfer ($n_{ad}$ and $n_c$) over $\rho$ differ from those of the other AMs.

Figure 3

(Color online) (a) Calculated effective binding distance $d_{eff}$ and (b) work functions $\left(W\right)$ of adatom-graphene systems. $d_{eff}$ was obtained by subtracting the ionic radii of the metal from the calculated adsorption distance. In (b), filled points denote the calculated $W$ on the adatom side, and open points denote calculated $W$ on the graphene layer side. $W$ for AMs except Li decreased with increasing $\rho$ along a common curve to a minimum at $\rho \approx 0.04$, but for Li it continued to decrease to a minimum at $\rho \approx 0.08$.

Figure 4

(Color online) (a) The plot in a plane perpendicular to graphene of charge density contributed by the states lying within the energy range from $-0.9\text{eV}$ up to the Fermi level in graphene with $2\times 2R0°$ adatom phase. Upper panel: Li; lower panel: K. Black dots indicate the position of adatoms. The scale bar has units of $\text{electron}/{\text{Å}}^3$. Li was more closely bound to graphene than were all other AMs (here only K is shown) that show a more uniform charge density compared to Li. (b) The electrostatic potential $\left(\varphi \right)$ of pristine graphene that should affect adatoms at their binding positions. This shows that Li will experience a significantly stronger potential than other AMs.