Substrate Mediated Long-Range Oscillatory Interaction between Adatoms: Cu/Cu(111)

Abstract

A quantitative study of the long-range interaction between single copper adatoms on Cu(111) mediated by the electrons in the two-dimensional surface-state band is presented. The interaction potential was determined by evaluating the distance distribution of two adatoms from a series of scanning tunneling microscopy images taken at temperatures of 9 -21 K. The long-range interaction is oscillatory with a period of half the Fermi wavelength and decays for larger distances d as 1͞d2 . Five potential minima were identified for separations of up to 70 Å. The interaction significantly changes the growth of Cu͞Cu(111) at low temperatures. PACS numbers: 68.35.Fx, 61.16.Ch Surface-state electrons on the close packed surfaces of noble metals form a two-dimensional nearly free electron gas. The scattering of the electrons off point defects and step edges generates standing wave patterns in the electron density, which can be directly observed with the scanning tunneling microscope (STM) [1]. Analysis of the standing wave patterns provides a direct way to determine the surface-state dispersion and the scattering properties of the scatterers [2,3]. The ability of single adatoms to scatter surface electrons can be used to confine electrons in so-called quantum corrals: artificial structures of single adatoms build up by atomic manipulation [4]. The previous studies on standing waves concentrated on the effects caused by the adatom scatterers on the surface electron gas. The twodimensional electron gas itself should, on the other hand, give rise to an interaction between the scatterers.The surface-state mediated interaction is long ranged and oscillatory in nature. The history of indirect interactions mediated by the substrate electrons began with the theoretical works of Grimley [5], and Einstein and Schrieffer [6,7], followed by the experimental works of Tsong [8], and Watanabe and Ehrlich [9], who used field ion microscopy to observe the long-range interaction between single metal adatoms adsorbed on a W(110) surface. The long-range interaction mediated by a two-dimensional electron gas was considered in 1978 by Lau and Kohn [10]. They showed that, in the special case of a partially filled surface-state band, the interaction energy decays very slowly, as 1͞d 2 for large separations and is oscillatory with a periodicity of half of the Fermi wavelength. Only recently a room temperature STM study discussed an indication of such a long-range interaction between strongly bonded sulfur atoms on a Cu(111) surface [11] and a few further qualitative investigations exist [12].Here we report the first detailed quantitative study of a long-range interaction mediated by a two-dimensional nearly free electron gas. We have determined the interaction energy between single Cu adatoms on a Cu(111) surface from extensive measurements of their mutual spatial correlations. Although the interaction is very weak, the very low diffusion barrier (40 meV) [13][14][15] for the adatoms enabled us to probe their interaction energy up to distances of ...

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