Many-Body Effects in Angle-Resolved Photoemission: Quasiparticle Energy and Lifetime of a Mo(110) Surface State

Abstract

In a high-resolution photoemission study of a Mo(110) surface state various contributions to the measured width and energy of the quasiparticle peak are investigated. Electron-phonon coupling, electron-electron interactions, and scattering from defects are all identified mechanisms responsible for the finite lifetime of a valence photohole. The electron-phonon induced mass enhancement and rapid change of the photohole lifetime near the Fermi level are observed for the first time. PACS numbers: 79.60.Bm, 73.20.At Recent investigations of strongly correlated electron systems have questioned the validity of one of the most fundamental paradigms in solid state physics-Fermi liquid theory. The latter picture is based on the existence of "quasiparticles," or single-particle-like low energy excitations which obey the exclusion principle and have lifetimes long enough to be considered as particles. Strictly speaking, the quasiparticle concept is restricted to zero temperature and a narrow region around the Fermi level [1], but its usefulness often continues to finite temperatures, and energies away from the Fermi level [2]. Indications for possible non-Fermi-liquid behavior have been found in some organic one-dimensional conductors [3] and in the normal state of high temperature superconductors [4]. A whole variety of experimental techniques have been employed in the search for such behavior, including resistivity measurements [5], infrared spectroscopy [6], scanning tunneling spectroscopy [7], and time-resolved two-photon photoemission [8]. Angle-resolved photoemission spectroscopy (ARPES) has an advantage, in that the energy and lifetime of the photohole are directly observable in the experiment. ARPES in principle measures the quasiparticle spectral function [9]:where´k represents the energy of the state in the Hartree potential, and S͑k, v͒ is the quasiparticle self-energy reflecting many-body interactions. Thus, momentum resolved self-energies are directly accessible in the experiment and, as such, ARPES represents a crucial experimental probe for the presence or absence of Fermi liquid behavior. Furthermore, complications connected to the lifetime of the photoelectron (in three-dimensional systems) may be overcome in quasi-low-dimensional systems. Indeed, there have already been several photoemission studies which quantitatively compare peak widths to calculated lifetimes for metallic surface states [10] and two-dimensional states in layered materials [11].When considering the lifetime of the valence hole, there are three main decay mechanisms: electron-electron scattering, electron-phonon scattering, and impurity (defect) scattering. In three-dimensional systems, the electronelectron interaction contributes to the total width or inverse lifetime with the term G e-e ͑v, T ͒ 2b͓͑pk B T ͒ 2 1 v 2 ͔. This scattering rate does not depend on the form of the interaction, but it may depend on the shape of the Fermi surface. If the scattering process is two dimensional, then the quadratic energy (temperature) dependence...

Decay of electronic excitations at metal surfaces

“…Also shown is the real part of the quasiparticle self-energy Re S, which is obtained by subtracting a straight line from the experimental dispersion curve shown in the insert. This procedure gives the electron-phonon term for the real part of the self-energy [138]. The solid line through 2jIm Sj in Fig.…”

“…24). Valla et al [138] studied a d-like surface state which disperses rapidly with polar angle y to E F . The important observations in our context are that: (i) the photoemission peak clearly sharpens up on going towards the Fermi level and (ii) there is a small but clearly resolved change in band velocity near E F , see the insert in Fig.…”

Photoemission as a Probe of the Collective Excitations in Condensed Matter Systems

“…Such behavior is indicative of the scattering of the photo-hole from some collective excitation or "mode" of the system. The striking similarity with the behavior observed in ARPES studies of a photo-hole interacting with phonons [16,17] would point to the electron-phonon coupling as the source of this behavior. However this would imply the presence of ∼ 70 meV phonons in the CDW state where the highest calculated and measured phonon frequency is ∼ 40 meV.…”

“…The measured widths also have an energy-independent contribution due to scattering from hydrogen impurity centers. [17] The calculated real component of the self energy, Σ 1 , derived through a Kramers Kronig transform of Σ 2 is also shown in figure 4 where it is compared with the experimentally derived values. From Σ 1 it is possible to determine a value for the electron-phonon coupling constant of 0.4 to be compared with the bulk value of 0.42.…”

“…Fig. 3 shows an image of the spectral intensity excited from a two-dimensional surface resonance in the Γ -N azimuth of a Mo(110) crystal with the sample held at 70 K. [17] The state shown in the figure corresponds to a surface resonance which closes an elliptical hole Fermi orbit around the center of the zone, Γ. [18] In the vicinity of the Fermi level there is a notable change in the rate of dispersion, or mass enhancement, and a rapid change in the width of the band.…”