1. Department of Physics and Material Science Program, University of New Hampshire, Durham, New Hampshire 03824, USA
2. CNISM and Dipartimento di Fisica, Università di Genova, 16146 Genova, Italy
3. Institute for Storage Ring Facilities and Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, 8000 Aarhus C, Denmark
4. Donostia International Physics Center (DIPC), Departamento de Fisica de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Ciencias Quimicas, UPV/EHU, 20018 San Sebastian, Spain
5. CIC nanoGUNE Consolider and Materia Kondentsatuaren Fisika Saila, UPV/EHU, Mikeletegi Pasealekua 56, E-2009 Donostia, Basque Country, Spain
6. Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, 28049 Madrid, Spain
7. IMEM-CNR and Dipartimento di Fisica, Università di Genova, 16146 Genova, Italy

Correspondence to: Karsten Pohl¹ Correspondence and requests for materials should be addressed to K.P. (Email: karsten.pohl@unh.edu).

Abstract

Nearly two-dimensional (2D) metallic systems formed in charge inversion layers¹ and artificial layered materials^{2, 3} permit the existence of low-energy collective excitations^{4, 5}, 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 phonons³, and because they might mediate the formation of Cooper pairs in high-transition-temperature superconductors⁶. 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 electrons⁷. Rather, metallic surfaces should support only conventional surface plasmons⁸—higher-energy modes that depend only on the electron density. Surface plasmons have important applications in microscopy^{9, 10} and sub-wavelength optics^{11, 12, 13}, 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.

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