Extremely confined quantum-well states for (2×2)-K and (3×3)-K on graphite: First-principles calculations

Abstract

We report on the atomic and electronic structure obtained by first-principles density functional theory calculations for a (2 x 2)-K monolayer as well as a (root 3 x root 3)-K monolayer on graphite represented by an 11-layer carbon slab. In both cases, the calculations predict that the K atoms reside above hollows [2.93 angstrom above the surface atomic layers for (2 x 2)-K]. The electronic structure is characterized by a partially occupied, free-electron-like overlayer quantum-well (QW)-state band (E(F) - 0.76 eV at (Gamma) over bar, 1.14m(e)) and one empty QW band (E(F) + 1.7 eV, 1.0m(e)), for (2 x 2)-K. The partially filled QW band, which has an energy and dispersion close to that which has been experimentally observed, provides examples of extremely confined states with nearly all charge (93%) deposited in the overlayer. In the substrate, the layer-confined sigma bands are rigidly downshifted, by 0.6 eV for the outermost carbon-atom layer and by 0.14 eV for the second layer. For the pi electrons, downshifted bands are split off from the ladder of closely spaced band energies, which approximate the continuum of states in a thick graphite sample. The splitting off can be regarded as the formation of a QW state, since the electrons are found mainly in the outermost layer of carbon atoms. The split-off band is not obtained via a downshift of the band with the lowest energy among the closely spaced states, since the band-edge states of the bare substrate have only a small amplitude in the outermost layer of carbon atoms. The high degree of confinement for both the K overlayer states and the C underlayer pi states should make the system of interest for studies of the excitations of two near-two-dimensional electron gases at short distance.