Anisotropic Dispersion and Partial Localization of Acoustic Surface Plasmons on an Atomically Stepped Surface: Au(788)

Abstract

Understanding acoustic surface plasmons (ASPs) in the presence of nanosized gratings is necessary for the development of future devices that couple light with ASPs. We show here by experiment and theory that two ASPs exist on Au(788), a vicinal surface with an ordered array of monoatomic steps. The ASPs propagate across the steps as long as their wavelength exceeds the terrace width, thereafter becoming localized. Our investigation identifies, for the first time, ASPs coupled with intersubband transitions involving multiple surface-state subbands. DOI: 10.1103/PhysRevLett.113.186804 PACS numbers: 78.68.+m, 73.20.At, 73.20.Mf, 79.20.Uv Acoustic surface plasmons (ASPs) originate from the excitation of a 2D electron gas whenever it is effectively screened by an underlying 3D electron gas [1]. Contrary to sheet plasmons, characterized by a square-root-like dependence on the wave vector [2], ASPs have a linear soundlike dispersion and hence frequency-independent group and phase velocities. These excitations are very promising for future applications in plasmonics because the speed, and thus the wavelength, of ASPs is 3 orders of magnitude lower than that of light, permitting us in principle to locate plasmonic excitations on the scale of a few nanometers. A hypothetical polychromatic ASP signal would indeed propagate without distortion, allowing for accurate signal processing.Suitable 2D electron gases are associated with the Shockley surface state (SSS) or any other 2D free electron gas. Linearly or quasilinearly dispersing ASPs have indeed been reported for bare and O-covered Be(0001) [3,4], Cu(111) [5,6], and Au(111) [7,8], as well as for graphene deposited on metal substrates. Generally speaking, they are expected to exist whenever two slightly spatially separated electron gases interact sufficiently strongly [9,10]. Ab initio density-response calculations [3,7,11] confirmed their existence on Be, Cu, Ag, and Au surfaces.The dispersion curves of ASP and light do not, however, per se cross at clean surfaces, so a momentum source is needed to realize coupling of the ASP with photons; this can be realized by, e.g., a grating. However, the short wavelength of the ASP requires realization of this grating on the atomic scale. For example, it can be generated by a regular array of atomic steps, as provided by vicinal surfaces of single crystals. Nanostructuring, however, implies concomitant generation of atomic defects, so it is necessary to understand how defects and confinement in nanosized regions modify the ASP dispersion. As a first step, we recently demonstrated that the ASP survives damage induced by heavy ion bombardment on Cu (111) [12], at least as long as the SSS itself survives the treatment. The question we address here is how the plasmonic structure of a bare Au(111) surface is transformed by a regular array of atomic steps. Combining experiment and density-response calculations, we demonstrate the existence of two plasmonic modes at the Au(788) surface both parallel and perpendicular to the steps, due...

Two-dimensional crossover and strong coupling of plasmon excitations in arrays of one-dimensional atomic wires

“…Such dispersions have indeed been found for regular arrays of atomic wires on insulating substrates [18][19][20]. Moreover, confinement effects in these metallic subunits on the surface lead to the formation of intersubband excitations [19][20][21].…”

“…Such dispersions have indeed been found for regular arrays of atomic wires on insulating substrates [18][19][20]. Moreover, confinement effects in these metallic subunits on the surface lead to the formation of intersubband excitations [19][20][21].Before realizing such visions, several fundamental properties of these quasi-1D plasmons need to be clarified, comprising, in particular, the question of dimensional crossover, but also the correct treatment of many-body effects, electronic correlations, and Coulomb screening [22][23][24]. These open topics led to a partly unsatisfactory description of experimental results in the past [18,19,25].…”

Origin of metallicity in atomic Ag wires on Si(557)

“…Because of their short wavelengths, they are interesting candidates for energy transfer and local energy transport on the nanoscale, since extreme localization compared with standard surface plasmon modes should be possible. Linear dispersion, necessary for undistorted signal transfer, can be achieved in these systems by coupling a two-dimensional electron gas (2DEG) with other two-(2D) or three-dimensional electron gases [9], as seen, e.g., for acoustic surface plasmons of Shockley type surface states on surfaces of noble metals, [10][11][12][13][14][15], or for graphene on metallic surfaces [16,17].…”

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.…”