Correlated Motion of Electrons on the Au(111) Surface: Anomalous Acoustic Surface-Plasmon Dispersion and Single-Particle Excitations

Abstract

The linear dispersion of the low-dimensional acoustic surface plasmon (ASP) opens perspectives in energy conversion, transport, and confinement far below optical frequencies. Although the ASP exists in a wide class of materials, ranging from metal surfaces and ultrathin films to graphene and topological insulators, its properties are still largely unexplored. Taking Au(111) as a model system, our combined experimental and theoretical study revealed an intriguing interplay between collective and single particle excitations, causing the ASP associated with the Shockley surface state to be embedded within the intraband transitions without losing its sharp character and linear dispersion. DOI: 10.1103/PhysRevLett.110.127405 PACS numbers: 78.68.+m, 71.45.Gm, 79.20.Uv One of the most attractive aspects of plasmonics-an explosively growing interdisciplinary research field-is the ability to squeeze light into subwavelength regions thanks to the properties of surface plasmon polaritons (SPP) [1,2], an excitation resulting from the interaction of photons with surface plasmons [3]. In particular, light confinement (i.e., the ratio between the wavelength of the electromagnetic radiation and of the induced plasmonic excitation) in the plane parallel to the surface takes place because of the several times lower velocity of the SPP with respect to light, implying that at any given excitation frequency, the wavelength of the SPP is shortened by the same ratio.Even higher in-plane confinements can be achieved with plasmons associated with a two dimensional electronic gas, notably in graphene [4], since their dispersion is much flatter than that of SPP. The 2D plasmon energy ! 2DP varies as $ ffiffiffiffiffi q k p for small in-plane momentum q k with ! 2DP ! 0 as q k ! 0 [5], which allows for extraordinary light confinement from subterahertz to midinfrared frequencies by use of appropriate nanostructures providing the necessary momentum transfer.Recently, an in-plane confinement rate as high as 40 was attained in graphene sheets grown on a dielectric substrate [6,7]. An even higher value of $100 was achieved for graphene nanostructures [8], making use of the 2D plasmon supported by the 2D electron gas of doped graphene. However, the $ ffiffiffiffiffi q k p dispersion makes a distortionless propagation of nonmonochromatic signals inherently impossible, since the different frequencies components propagate at different velocities. This drawback can be overcome using a plasmon energy with a linear rather than a square root dispersion. The former is expected whenever a partially filled electronic 2D band is coupled and shielded by other 2D or 3D electron gases [9], and is thus a fairly general concept. This is, in particular, the case for metal surfaces supporting an electronic Shockley surface state (SS) with band dispersion crossing the Fermi level [10]. Such a mode, called an acoustic surface plasmon (ASP), was observed, in addition to the conventional surface plasmons, for a variety of noble and simple metal surfaces [11][12][...

Direct observation of many-body charge density oscillations in a two-dimensional electron gas

“…31), in the considered 2D electron system the collective-excitation mode has a linear dispersion o pl q ð Þ $ q due to screening by the underlying three-dimensional electron system 25 . This mode is the aforementioned ASP, which was predicted to exist at metal surfaces with a partly occupied surface-state band 25,26 and was recently observed on Be 32 , Cu 33,34 and Au 35,36 surfaces by electron-energy-loss spectroscopy.…”

Photoemission footprints of extrinsic plasmarons

“…Later on Electron Energy Loss Spectroscopy experiments have confirmed the presence of the ASP mode at the Be(0001) [5,6] and noble metal surfaces [7][8][9][10][11][12][13][14] in good agreement with calculations and graphene adsorbed on metal substrates [15][16][17][18][19][20][21][22]. In cases when surface localized quantum well states are formed, e.g.…”

Electron energy loss and inelastic x-ray scattering cross sections from time-dependent density-functional perturbation theory

“…Although some attempts to investigate EEL and IXS spectra using many-body perturbation theory have been made, [24][25][26][27] the vast majority of the studies existing to date relies on TDDFT, which in fact has been successfully used to study plasmons in a number of bulk and surface [9][10][11][12][13][14] systems.…”