Nearly two-dimensional (2D) metallic systems formed in charge inversion layers1 and artificial layered materials2,3 permit the existence of low-energy collective excitations4,5, 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 microscopy9,10 and sub-wavelength optics11,12,13, 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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Allen, S. J., Tsui, D. C. & Logan, R. A. Observation of the two-dimensional plasmon in silicon inversion layers. Phys. Rev. Lett. 38, 980–983 (1977)
Nagao, T., Hildebrandt, T., Henzler, M. & Hasegawa, S. Dispersion and damping of a two-dimensional plasmon in a metallic surface-state band. Phys. Rev. Lett. 86, 5747–5750 (2001)
March, N. H. & Tosi, M. P. Collective effects in condensed conducting phase including low-dimensional systems. Adv. Phys. 44, 299–386 (1995)
Stern, F. Polarizability of a two-dimensional electron gas. Phys. Rev. Lett. 18, 546–548 (1967)
Chaplik, A. V. Possible crystallization of charge carriers in low-density inversion layers. Sov. Phys. JETP 35, 395–398 (1972)
Ruvalds, J. Are plasmons the key to superconducting oxides? Nature 328, 299 (1987)
Sarma, S. D. & Madhukar, A. Collective modes of spatially separated, two-component, two-dimensional plasma in solids. Phys. Rev. B 23, 805–815 (1981)
Ritchie, R. H. Plasma losses by fast electrons in thin films. Phys. Rev. 106, 874–881 (1957)
Schuster, S. C., Swanson, R. V., Alex, L. A., Bourret, R. B. & Simon, M. I. Assembly and function of a quaternary signal transduction complex monitored by surface plasmon resonance. Nature 365, 343–347 (1993)
Flatgen, G. et al. Two-dimensional imaging of potential waves in electrochemical systems by surface plasmon microscopy. Science 269, 668–671 (1995)
Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824–830 (2003)
Lezec, H. et al. Beaming light from a subwavelength aperture. Science 297, 820–822 (2002)
Pendry, J. Playing tricks with light. Science 285, 1687–1688 (1999)
Rocca, M., Valbusa, U., Gussoni, A., Maloberti, G. & Racca, L. Apparatus for adsorption studies. Rev. Sci. Instrum. 62, 2172–2176 (1991)
Höchst, H., Steiner, P. & Hüfner, S. The conduction electron hole coupling in beryllium metal. Phys. Lett. 60A, 69–71 (1977)
Silkin, V. M. et al. Novel low-energy collective excitation at metal surfaces. Europhys. Lett. 66, 260–264 (2004)
Rocca, M. Low-energy EELS investigation of surface electronic excitations on metals. Surf. Sci. Rep. 22, 1–71 (1995)
Persson, B. N. J. & Zaremba, E. Electron-hole pair production at metal surfaces. Phys. Rev. B 31, 1863–1872 (1985)
Liebsch, A. Electronic Excitations at Metal Surfaces (Plenum, London, 1997)
Karlsson, U. O., Flodström, S. A., Engelhardt, R., Gädeke, W. & Koch, E. E. Intrinsic surface state on Be(0001). Solid State Commun. 49, 711–714 (1984)
Bartynski, R. A., Jensen, E., Gustafsson, T. & Plummer, E. W. Angle-resolved photoemission investigation of the electronic structure of Be: Surface states. Phys. Rev. B 32, 1921–1926 (1985)
Chulkov, E. V., Silkin, V. M. & Shirykalov, E. N. Surface electronic structure of Be(0001) and Mg(0001). Surf. Sci. 188, 287–300 (1987)
Silkin, V. M., Pitarke, J. M., Chulkov, E. V. & Echenique, P. M. Acoustic surface plasmons in the noble metals Cu, Ag, and Au. Phys. Rev. B 72, 115435–115441 (2005)
Politano, A., Chiarello, G., Formoso, V., Agostino, R. & Colavita, E. Plasmon of Shockley surface states in Cu(111): A high-resolution electron energy loss spectroscopy study. Phys. Rev. B 74, 081401(R) (2006)
This work was supported by the National Science Foundation (B.D. and K.P.); Compagnia di San Paolo (L.V., L.S. and M.R.); the Departamento de Educaion, Universidades e Investigacion del Gobierno Vasco and the University of the Basque Country UPV/EHU; the Spanish MEC (V.M.S., J.M.P., E.V.C., P.M.E. and D.F.); the Danish Natural Science Research Council (P.H.); and by the Programa Ramon y Cajal and Comunidad de Madrid (D.F.).
Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.
This file contains Supplementary Notes divided into the following sections: A. Ab initio calculation details; B. Extraction of the experimental dispersion; C. Oxygen influence on the Acoustic Surface Plasmon and Supplementary Figures 1-3 with Legends. (PDF 853 kb)
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Journal of the Optical Society of America B (2019)
Nano Letters (2019)
Physical Review B (2019)
Physical Review B (2019)
Physical Review B (2018)