# Focus: Surfing in an Atom’s Wake

Published September 26, 2000  |  Phys. Rev. Focus 6, 14 (2000)  |  DOI: 10.1103/PhysRevFocus.6.14

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

Jascha Repp, Francesca Moresco, Gerhard Meyer, Karl-Heinz Rieder, Per Hyldgaard, and Mats Persson

Published October 2, 2000

In 1993, physicists at IBM created the picturesque “quantum corral” by placing 48 iron atoms in a circle on a copper surface. The famous images dramatically displayed the standing waves made by surface electrons inside the corral. Now, in the 2 October PRL, a team shows that these same waves allow atoms dropped on the surface to interact with one another over long distances. Their scanning tunneling microscope (STM) data show that this electron-mediated force is oscillatory in space–alternately attractive and repulsive as one atom “rides” the electron waves produced by the other. The interaction leads to rings of attraction and repulsion surrounding each atom, so the results may improve understanding of the formation of atomic-scale structures on surfaces.

Theories dating back to 1967 have suggested that electrons in a metal generate so-called indirect interactions between adatoms–atoms sitting on a surface that aren’t part of the solid’s crystal structure. A 1978 paper by Nobel Laureate Walter Kohn of the University of California, Santa Barbara, and K. H. Lau predicted that, if the electrons are in specific quantum states at the surface, the force diminishes with the inverse square of the distance between the adatoms–a much longer-range interaction than exists otherwise. Lau and Kohn also expected the force to be oscillatory (similar to other indirect interactions), with a period related to the surface electrons’ wavelength. Under these conditions, the potential energy surface surrounding each adatom looks something like a still picture of the circular waves around a stone thrown in a pond. The wavelike surface electrons scattering from the adatom create ring-shaped troughs of attraction in the potential energy function, and neighboring adatoms are most likely to collect at these troughs. Until now, no one had directly measured this unusual long-range, oscillatory interaction predicted by Lau and Kohn.

The problem, explains Gerhard Meyer of the Free University of Berlin (FUB), is that these long-range forces between adatoms are so weak; the corresponding energies are less than 1 meV. Meyer is part of a team that captured the oscillatory interaction by taking 3400 STM images of copper adatoms on a copper surface at temperatures between 9 and 21 K. They waited 30 seconds between images to allow the adatoms to hop to new positions. For each image the team measured the distances between isolated pairs of adatoms and collected a large histogram showing the likelihood of each separation distance, from 0 to 7.5 nm. “What you see is that certain distances are preferred,” says Meyer.

The team, led by FUB’s Karl-Heinz Rieder, found an oscillatory potential energy function as one moves away from an adatom, with a period (1.5 nm) and decay rate (inverse square) in agreement with the 1978 predictions. To further verify their results, the team used the STM to directly image the electron waves surrounding pairs of adatoms. The properties of the scattered electron waves were in rough agreement with the authors’ theoretical predictions.

“I was thrilled” to see the paper, says Ted Einstein of the University of Maryland in College Park. Although there have been other hints of the effect, he says, “this is really clear-cut and beautiful.” Einstein points out that it is unusual for an oscillatory interaction to be so long-ranged and to have circular symmetry and says it might have practical consequences for interactions between single-atom-high steps in atomic-scale devices.