Surface-state mediated three-adsorbate interaction: electronic nature and nanoscale consequences

The interaction energy of a three-adsorbate cluster on a surface consists of the sum of pair interactions plus a trio contribution. The trio interaction is produced by interference of electrons which propagate around the cluster perimeter, d123. We investigate such interactions for a noble-metal (1 1 1) surface, where the isotropic Shockley surface-state band produces cluster-interaction energies significant for the low-temperature adsorbate dynamics. We provide experimentally testable interaction-energy predictions, specified by the s-wave phase shift δF that characterizes the standing-wave patterns seen in scanning-tunneling microscopy (STM) images. Compared with the adsorbate-pair interactions, the trio contribution exhibits a slightly weaker amplitude and a slightly faster asymptotic decay. We discuss how the trio interaction can affect the cluster geometry by introducing an additional angular dependence in the adsorbate interaction.