Low-energy acoustic plasmons at metal surfaces

Abstract

Nearly two-dimensional (2D) metallic systems formed in charge inversion layers and artificial layered materials permit the existence of low-energy collective excitations, called 2D plasmons, which are not found in a three-dimensional (3D) metal. These excitations have caused considerable interest because their low energy allows them to participate in many dynamical processes involving electrons and phonons, and because they might mediate the formation of Cooper pairs in high-transition-temperature superconductors. Metals often support electronic states that are confined to the surface, forming a nearly 2D electron-density layer. However, it was argued that these systems could not support low-energy collective excitations because they would be screened out by the underlying bulk electrons. Rather, metallic surfaces should support only conventional surface plasmons-higher-energy modes that depend only on the electron density. Surface plasmons have important applications in microscopy and sub-wavelength optics, but have no relevance to the low-energy dynamics. Here we show that, in contrast to expectations, a low-energy collective excitation mode can be found on bare metal surfaces. The mode has an acoustic (linear) dispersion, different to the dependence of a 2D plasmon, and was observed on Be(0001) using angle-resolved electron energy loss spectroscopy. First-principles calculations show that it is caused by the coexistence of a partially occupied quasi-2D surface-state band with the underlying 3D bulk electron continuum and also that the non-local character of the dielectric function prevents it from being screened out by the 3D states. The acoustic plasmon reported here has a very general character and should be present on many metal surfaces. Furthermore, its acoustic dispersion allows the confinement of light on small surface areas and in a broad frequency range, which is relevant for nano-optics and photonics applications.

Plasmons in nanoscale and atomic-scale systems

“…the regions where bulk electrons (3D electron gas) attempt to screen the charge disbalance in the 2D system. The observation of this mode by EELS was first reported for the Be(0001) surface [51] and later for Au(111) [53] and Cu(111) surfaces [54].…”

One-dimensional plasmons in ultrathin metallic silicide wires of finite width

“…It is therefore crucial for structure and array formation, as also demonstrated below. This scenario is very different from the formation of 2D acoustic surface plasmons generated by partially filled surface states of bulk metals, 13,14 where the response of the bulk metal electrons has to be taken into account.…”

Electron-phonon coupling in a system with broken symmetry: Surface ofBe(0001)

“…The depth penetration of a surface state depends upon how far it is removed from closest bulk band edge [11]. Moreover, it has been reported that the interplay between the surface electronic states and the bulk electronic states in the same region of the space (near the surface) could result in acoustic surface plasmon due to charge oscillation between the 2D and 3D subsystems [15].…”