We report on long-range interactions between adsorbates on metal surfaces with a surface state. A comparison of three adsorbate/substrate systems [Cu/Cu(111), Co/Cu(111), and Co/Ag(111)] suggests the general existence of such interactions and shows up common characteristics. In all cases, the interaction energy $E\left(r\right)\mathrm{}$ manifests itself up to a distance of 60 Å, decays as ${1/r}^2,$ and oscillates with a period of ${\lambda }_{\mathrm{F}}/2.\mathrm{}$ Our data are in excellent agreement with theory and establish the link between the spatial variation of the interaction energy and the adsorbate scattering properties. We demonstrate that the long-range interactions stabilize an ordered two-dimensional (2D) gas of adsorbates and thus create states of dilute 2D matter.

• Received 2 November 2001

DOI:https://doi.org/10.1103/PhysRevB.65.115420