Dimensionality Effects in the Lifetime of Surface States

Abstract

A long-standing discrepancy between experimental and theoretical values for the lifetimes of holes in the surface-state electron bands on noble metal surfaces is resolved; previous determinations of both are found to have been in error. The ability of the scanning tunneling microscope to verify surface quality before taking spectroscopic measurements is used to remove the effects of defect scattering on experimental lifetimes, found to have been a significant contribution to prior determinations. A theoretical treatment of inelastic electron-electron scattering is developed that explicitly includes intraband transitions within the surface state band. In our model, two-dimensional decay channels dominate the electron-electron interactions that contribute to the hole decay and are screened by the electron states of the underlying three-dimensional electron system.

Decay of electronic excitations at metal surfaces

“…We also note from this figure that a large contribution from intraband transitions, strongly screened by the underlying 3D bulk electron system, is responsible for the large differences between the 3D free-electron gas prediction and the experimental results (represented by open triangles), as discussed in Ref. [52]. Calculations based on a pure 2D electron-gas model to describe the surface state give results that are much larger than the model-potential intraband contribution to the decay rate by factors of $7 for the state at the G point in Cu (1 1 1) and by a factor of $2.5 in Be(0 0 0 1).…”

“…This assumption is valid for image-potential states since their wave functions lie mainly at the vacuum side of the surface and the electron moves, therefore, in a region with little potential variation in a plane parallel to the surface. Moreover, this assumption is still reasonably good for the clear s-p z surface states on clean metal surfaces [52][53][54][55][56] and surfaces covered with alkali-metal adlayers [57], because these states do not show either a strong variation in the direction parallel to the surface region [58][59][60][61][62][63][64][65][66].…”

“…0Þ for Ag, Au and Cu are 4, 6.6 and 5.6, respectively [52,75]. García-Lekue et al [75] have analyzed the impact of d-electron screening and concluded that, in the long-wavelength limit (q !…”

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

“…Recently, it has been further expanded to study spin-split surface states on surface alloys 10 and topological insulators 11,12 . QPI has proven to be a powerful method to analyse electronic properties, such as energy dispersion relations 13 , lifetimes [14][15][16] , scattering phase shifts 1,7 , coherence lengths 9 and scattering channels 10,11,12 . One of the fundamental aspects of the QPI mapping is that in real space the amplitude of the LDOS oscillations reduces as the tip is moved away from the scattering centres.…”

“…One of the fundamental aspects of the QPI mapping is that in real space the amplitude of the LDOS oscillations reduces as the tip is moved away from the scattering centres. In part, this reduction is due to many-body inelastic decay [14][15][16] , since the injected quasiparticle, after a typical lifetime of several femtoseconds 17 (1 fs ¼ 10 À 15 s), eventually relaxes into states closer to the Fermi level E F . In reciprocal space, this finite lifetime results in a broadening of the peaks related to the LDOS oscillation wavevectors in Fourier transformed (FT) QPI maps 18 .…”