Density functional study of alkali-metal atoms and monolayers on graphite (0001)

Alkali-metal atoms (Li, Na, K, Rb, Cs), dimers, and $(2\ifmmode\times\else\texttimes\fi{}2)$ monolayers on a graphite (0001) surface have been studied using density functional theory, pseudopotentials, and a periodic substrate. The adatoms bind at the hollow site (graphite hexagon), with Li lying closest to $(1.84\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$ and Cs farthest $(3.75\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$ from the surface. The adsorption energies range between 0.55 and $1.21\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, and the energy ordering of the alkali-metal adatoms is $\mathrm{Li}>\mathrm{Cs}\ensuremath{\geqslant}\mathrm{Rb}\ensuremath{\geqslant}\mathrm{K}>\mathrm{Na}$. The small diffusion barriers ($0.02--0.21\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for the C-C bridge) decrease as the atom size increases, indicating a flat potential energy surface. The formation (cohesion) energies of $(2\ifmmode\times\else\texttimes\fi{}2)$ monolayers range between 0.55 and $0.81\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, where K has the largest value, and increased coverage weakens the adsorbate-substrate interaction (decoupling) while a two-dimensional metallic film is formed. Analysis of the charge density redistribution upon adsorption shows that the alkali-metal adatoms donate a charge of $(0.4--0.5)e$ to graphite and the corresponding values for $(2\ifmmode\times\else\texttimes\fi{}2)$ monolayers are $\ensuremath{\sim}0.1e$ per atom. The transferred charge resides mostly in the $\ensuremath{\pi}$ bands (atomic ${p}_{z}$ orbitals) of the outermost graphene layer.