Controlled confinement of electron vacuum states through atomic engineering

Metal interfaces with a surface-projected band gap can host localized electronic states at the vacuum level: field emission resonances. While these states arise from confinement in the direction perpendicular to the surface, they are typically unconfined in the remaining directions. Here, we use atom manipulation of surface vacancies in a chlorine-terminated Cu(100) surface to engineer lateral confinement: we arrange the vacancies to reveal square patches of the underlying metal surface, creating atomically precise potential wells that host particle-in-a-box modes. The quantum numbers of these states can be tuned by adjusting the shape and size of the confined patches, making them attractive candidates as artificial quantum dots. The added confinement also renders the wavevector, k, a bad quantum number in all directions, thereby creating direct tunnelling paths from the vacuum-localized resonance to the bulk crystal that do not exist otherwise. As such, the resonances become critically dependent on the bulk band structure, resulting in negative differential resistance in the voltage range in which the band edge is upward sloping. Our results provide possible avenues for engineering atomic-scale resonant tunnelling diodes, which exhibit similar current-voltage characteristics.