Surface-state mediated three-adsorbate interaction: exact and numerical results and simple asymptotic expression

Journal article, 2003

The interaction energy of three adsorbates on a surface consists of the sum of the three-pair interactions plus a trio contribution produced primarily by interference of electrons which traverse the entire perimeter, d123, of the three-adsorbate cluster. Here, we investigate this three-adatom interaction when mediated by the isotropic Shockley surface-state band found on noble-metal (1 1 1) surfaces, extending work on pair interactions. Our experimentally testable result depends on the s-wave phase-shift, characterizing the standing-wave patterns seen in scanning-tunneling microscopy (STM) images. Compared with the adsorbate–pair interactions, and in contrast to bulk-mediated interactions, the trio contribution exhibits a slightly weaker amplitude and a slightly faster asymptotic envelope decay, d123−5/2. It also has a different but well-defined oscillation period dependent on d123 and little dependence on the shape of the cluster. We finally compare the asymptotic description with exact model calculations assuming short-range interactions, which are viable even in the non-asymptotic range (when not outweighed by bulk-mediated interactions).