Electronic surface states in beryllium

The Γ–M Be surface state found in two recent experiments is confirmed to be highly localized by a study of local density electronic states near the Fermi level of ultrathin Be films (n layers with n=1, 2, and 3). For n=3, a state at Γ is found 2.0 eV below ${\varepsilon }_F$ (experiment: 2.8 eV) and 1.9 eV above the film level which corresponds to the bulk band edge (experiment: 2.0 eV); good agreement in view of known limitations of local-density-approximation one-electron energies. That state at Γ falls in energy and its intersection with ${\varepsilon }_F$ along both Γ–M and Γ–K moves out from Γ with increasing n. The n-layer occupied states at M are not uniquely identifiable with either pure bulk or pure surface states, this is again in agreement with experimental indications that they are rather delocalized (as opposed to the one at Γ). The surface core-level 1s shift is estimated from the three-layer film (the thinnest system which can exhibit such a shift) as 0.21 eV (experiment: 0.50 eV). Previous restricted Hartree-Fock calculations on bulk and ultrathin-film Be differ markedly both from these results and from experiment; the discrepancies and their sources are considered.