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

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 $1/d^2$. Five potential minima were identified for separations of up to 70 Å. The interaction significantly changes the growth of Cu/Cu(111) at low temperatures.