Photoemission Study of a Strongly Coupled Electron-Phonon System

Abstract

We present high-resolution photoemission experiments of the G-surface state of Be(0001). The spectral function near the Fermi wave vector reveals a strong quasiparticle peak due to coupling with surface phonon modes. The coupling constant l is estimated to be 1.18 6 0.07 based on the renormalization of the effective mass. No gap was observed down to 12 K. Any interpretation of the data based on charge density wave formation or surface superconductivity can therefore be discarded.It has been recognized for many years that the surfaces of Be have a behavior contrasting the bulk properties of this metal. The electronic structure of Be metal is dominated by the fraction of 2s electrons promoted to 2p states, leading to severe deviations from the freeelectron model. Some examples are an unusually high Debye temperature and Poisson's ratio [1], as well as a large diamagnetic susceptibility and a small electronic contribution to the specific heat [2]. From bulk band structure calculations it is known that the Fermi level is situated in a dip in the density of states [2,3], leading to a number of states at E F an order of magnitude less than for other simple metals, e.g., Mg [3].The (0001) surface of Be does not reconstruct, but drastic modification of the bulk properties can be anticipated from the reduction in coordination at the surface. Lowenergy electron diffraction (LEED) measurements reveal large deviations of the interplanar spacing at the surface compared to the bulk. Large values for the mean square displacement and thermal expansion are also unveiled [4], and all of these physical parameters are well described by density-functional theory [5]. The surface phonon modes investigated by electron-energy-loss spectroscopy (EELS) could only be reproduced by calculations which assume substantial variations of the nearest neighbor force constants, inducing in the surface layer a reduction of the interplanar bonding and an increase of the in-plane bonding [3,6]. A detailed calculation of the electronic structure of Be (0001) [7] predicts the existence of surface states in gaps of the projected bulk density of states (DOS), in good agreement with angle-resolved photoemission data [8,9]. The charge density originating from the surface states is essentially localized within the first two layers [7,10] and dominates the DOS at E F by a factor of 4 over the bulk density. As a consequence of the valence charge redistribution, the binding energy of the 1s core level, which probes the local charge density [10], is shifted with respect to its bulk value. Four distinct components resolved by x-ray photoemission spectroscopy could be related to emission from layers at different depths below the surface [11]. Finally, the electron inelastic mean free path of 2 Å at low kinetic energies (10-40 eV) is anomalously small compared to about 10 Å of the universal curve due to a high electronhole pair and/or surface plasmon creation rate [12].The G-surface state of Be(0001) is widely decoupled from the bulk states and forms a nearly ideal...

Decay of electronic excitations at metal surfaces

“…For more details on theory and the interpretation of Im S concerning the G surface states on noble metals see Section 6.1. An even larger contribution of S is to be expected for the surfaces of Be, where ho m ¼ 70 meV and the coupling parameter l on Be(0 0 0 1) is estimated between 0:7 AE 0:1 [126], 1.15 [140] and 1.18 [141,142]. Strong contribution to G ep is indeed observed and will be discussed in the following.…”

“…to the noble metals. Very highresolution lineshape results on the G surface state were presented first by Hengsberger et al [141,142], with data taken at T ¼ 12 K and resolution parameters DE ¼ 5 meV and Dy ¼ 0:2 (in the direction of strong dispersion), respectively. They determine the initial state energy E i ¼ À2:73 eV at G, and effective masses m à =m ¼ 1:19 (along GM) and m à =m ¼ 1:14 (GK).…”

“…They determine the initial state energy E i ¼ À2:73 eV at G, and effective masses m à =m ¼ 1:19 (along GM) and m à =m ¼ 1:14 (GK). Hengsberger et al [141,142] demonstrated that the surface state is drastically modified near E F by the electron-phonon interaction. In particular, the lineshape near E F is no longer a Lorentzian: as the surface state approaches E F , a second peak appears at E i % À70 meV.…”

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.…”

“…Hengsberger et al found a similar value, λ = 1.18, for the electron-phonon coupling parameter in the surface region of Be by measuring the velocity renormalization in the surface band. [16] However the most recent study of the same surface reduced the value λ to 0.7, a value obtained from a determination of the rate of change of the real part of the self-energy,− (∂Σ 1 /∂ω), in the vicinity of E F . Enhanced values of λ have led to speculation on the possibility of enhanced superconducting transition temperatures in the surface region.…”