Charge-density oscillations at (1 1 1) noble metal surfaces

Induced charge-density oscillations at noble metal surfaces caused by an external static impurity are studied within linear response theory. The calculation takes into account such properties of realistic surface electronic structure as an energy gap for three-dimensional (3D) bulk electrons and a s − p_z surface state that forms two-dimensional (2D) electron system. It is demonstrated that the coexistence of these 2D and 3D electron systems has profound impact on the induced charge-density in the surface region. Thus, the oscillations with the 1/R² decay as a function of lateral distance, R, are established in both electron systems with characteristic chess-board-like structure. Additionally, the charge-density penetrates into the solid at a finite angle with respect to the surface normal in contrast to that in jellium model. The origin of both these findings is investigated.