Measurement and Qualitative Explanation of Decay Lengths of Attractive and Repulsive Forces between Natural and Artificial Atoms

TL;DR

This study measures and explains the decay lengths of attractive and repulsive forces between artificial quantum structures and probes, revealing differences from natural atoms and implications for atomic-scale device design.

Contribution

It provides the first quantitative comparison of decay lengths of forces in artificial quantum corrals versus natural atoms, linking decay length differences to electronic state localization.

Findings

Repulsive force decay length: 46 pm

Attractive force decay length: 66 pm

Natural atoms have shorter decay lengths than quantum corrals

Abstract

Artificial atoms, such as quantum corrals, offer an excellent platform to study fundamental interactions between localized quantum states and nanoscale probes. We performed atomic force microscopy measurements inside square quantum corrals on Cu(111) using CO- and metal-terminated tips. Using chemically unreactive CO-terminated tips repulsive Pauli forces can be probed, while metallic tips are attracted to the localized quantum states due to chemical bonding. We found distinct exponential decay constants of 46 pm for the repulsive and 66 pm for the attractive forces. Attractive and repulsive interactions between two natural atoms show significantly shorter decay lengths. While natural atoms feature states with a broad range of decay lengths, including very short ones from deeply bound states, quantum corrals are lacking such deeply bound and highly localized states, resulting in longer decay lengths. These results offer a new route to understand and design atomic-scale interactions in low-dimensional quantum structures and devices.