Probing Hot-Electron Dynamics at Surfaces with a Cold Scanning Tunneling Microscope

Abstract

We report on a novel approach to measure the phase relaxation length and femtosecond lifetime of hot quasiparticles on metal surfaces. A 4 K scanning tunneling microscope has been used to study the spatial decay of interference patterns in the local density of states for surface state electrons on Ag(111) and Cu(111). This decay is governed by inelastic electron-electron scattering. We find a ͑E 2 E F ͒ 22 energy dependence of the lifetimes for both Ag and Cu, and our values are comparable to the corresponding bulk electron lifetimes. This indicates that electron-electron interaction of hot surface state electrons with the Fermi sea is dominated by the underlying bulk electrons.[S0031-9007 (99)09260-1] PACS numbers: 73.20.At, 61.16.Ch, 72.10.Fk, 72.15.LhThe phase relaxation length L f , i.e., the distance a quasiparticle can propagate without losing its phase memory, is a key quantity in solid state physics. Quantum mechanical interference phenomena can prevail only if L f is larger than any other relevant length scale [1]. Examples include Aharonov-Bohm oscillations, quantum Hall effect, Friedel oscillations, and localization. With respect to surface physics, L f -or equivalently the lifetime t f of the quasiparticle-is of particular interest, since it governs the dynamics of charge transfer and electronic excitations in surface chemistry [2].Elegant experiments have been performed to determine

Decay of electronic excitations at metal surfaces

“…Below the Fermi energy (E ¼ 0) G approaches the value obtained previously from spectra taken on clean terraces (6 meV) [52] (Section 4.2). There is a clear increase of G at large energies, with GðE ¼ 0:5 eVÞ $ 40 meV, which is comparable with an extrapolation down to this energy of data for the Ag(1 1 1) surface state extracted from the spatial coherence of interference patterns at energies E > 1 eV by Bürgi et al [202] (Section 4.3.1). Finally, at energies close to E F a decrease of G reflects an increased lifetime of the corresponding quasiparticles (inset in Fig.…”

“…This lead the authors of Ref. [202] to conclude that the surface-state lifetimes are determined by scattering from bulk electronic states. It is important to note that some of the lifetimes reported, e.g.…”

“…By a quantitative analysis of these patterns Bürgi et al [202] succeeded in extracting L for surface-state electrons on Ag(1 1 1) and Cu(1 1 1) over a range of energies above the Fermi level. summarizes characteristic data recorded at two different sample bias voltages, 1 V (top) and 2 V (bottom), near a downward monatomic step on Cu (1 1 1).…”

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 .…”