Time-dependent screening of a point charge at a metal surface

Abstract

The space-time evolution of the dynamical screening charge density caused by a suddenly created point charge at the Cu(111) surface is investigated in the linear response approximation. Considering a thin slab as a model for the Cu(111) surface, we investigate the confinement effects on dynamical screening as well. The results have been obtained on the basis of self-consistent evaluation of the energy-momentum-dependent response function, taking into account the realistic surface band structure of Cu(111). At the initial stage, we observe fast long-range charge density oscillations due to excitation of the surface plasmon modes. Then we observe the propagation of the shock wave of the electron-hole excitations along the slab with velocity determined by the Fermi velocity of bulk Cu. At longer times, we have identified the propagation along the two slab surfaces of a much slower (with velocity ∼ 0.3 au, close to the Fermi velocity of the Cu(111) surface state) charge disturbance due to acoustic surface plasmon. The role of the energy band gap in the direction perpendicular to the surface in establishing the screening is also addressed.

Landau damping of quantum plasmons in metal nanostructures

“…In this study, we first use the real-space RPA approach to evaluate electron density-density responses [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Furthermore, we also use the e-h pair basis set [41][42][43][44][45][46][47][48][49] to evaluate the state-state responses in order to reveal the underlying composition of the plasmon resonance.…”

Ultrafast electronic response of Ag(111) and Cu(111) surfaces: From early excitonic transients to saturated image potential

“…For metallic densities of practical interest the major part of the screening charge is localized within a few atomic radii of the surface region, with the induced charge density or Friedel oscillations extending deeper into the bulk. [6][7][8][9][10][11][12][13] It also turns out that for perturbations induced by external charge spatially restricted outside the equilibrium surface electronic charge density, the self-consistent linear response provides a complete picture of screening which has a classical analog in the form of image charge. 6,8,11 Early theoretical studies of the screening properties of surfaces were focused mainly on the energetic and spatial aspects of the induced and image charge which proved accessible by the then available experimental techniques (for review see Chapters 2 and 3 in Ref.…”

“…[12,13,47] we have set foundations for a theoretical description of the temporal and spatial evolution of the induced screening charge and ensuing potentials, respectively, and applied it to the Cu(111) surface. The latter is considered as a prototype system for demonstrating the existence of well defined SS-and IP-band states on metals, both experimentally and theoretically.…”

Nonlinear Plasmonic Photoelectron Response of Ag(111)

“…The complex dielectric tensor ε(w) defines how electrons in a metal experience an optical field and participate in the nonlinear electro-optic response. The epsilon near zero (ENZ; Re[ε(w)]=0) condition defines the bulk plasmon frequency, wp, and marks an abrupt change in light-matter interactions in solids [1][2][3][4][5][6][7][8][9][10]. The ENZ condition is intrinsic to metals [11][12][13][14], but also defines the optical properties of doped semiconductors [15], optical phonons, and metamaterials [16,17]; it designates a frequency region where the reflectivity drops to a minimum and the dielectric response at surfaces is nonlocal [11,[18][19][20], and dominantly nonlinear [15,16,21,22].…”