Surface-state–mediated three-adsorbate interaction

The interaction energy of three adsorbates on a surface consists of the sum of the three pair interactions plus a trio contribution produced by interference of electrons which propagate the entire perimeter, d123, of the three-adsorbate cluster. Here we investigate this triple-adsorbate interaction that is mediated by the isotropic Shockley surface-state band found on noble-metal (111) surfaces. Our experimentally testable result depends on the s-wave phase shift, $\delta_\ab{F}\neq 0$, 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 has a slightly weaker amplitude and asymptotically decays slightly faster, $\propto d_{123}^{-5/2}$. It also has a distinctive oscillation period dependent on d123. We finally compare the asymptotic description with exact model calculations.