Phonon contribution to quasiparticle lifetimes in Cu measured by angle-resolved photoemission

Abstract

The line shape of the photoelectron spectrum emitted from the sp-derived surface state at I on Cu(111) is investigated. The line shape is Lorentzian, and the temperature dependence of the width is linear, varying from 30 meV at 30 K to 75 meV at 625 K. Less than 5-rneV variation with binding energy is observed. The temperature dependence is explained as the phonon contribution to the inverse hole lifetime, predicted to be 2~kkbT allowing the determination that the electron-phonon mass enhancement parameter X. = 0.14~0.02 for this surface state at I . This is compared to X =0.15 reported as an average over the bulk Fermi surface.In the standard picture of angle-resolved photoemission spectroscopy, the peak width observed from a perfect crystal with negligible dispersion of the hole state perpendicular to the surface is equal to the inverse hole lifetime fi, /r. ' A measurement of linewidth as a function of binding energy, temperature, and impurity concentration determines the dependence of the hole lifetime on these variables. If the measurements are done at hole energies relatively close to the Fermi energy EF then one can compare to determinations based on low-energy techniques, such as Fermi surface probes, conductivity, and specific-heat measurements. The photoemission measurement is in many ways superior to these other techniques. It is more direct, involves no Fermi surface averaging, and does not depend on assumptions about one-electron theory. Photoemission also has the unique advantage that the energy dependence of the lifetime is directly observable. Its well-known surface sensitivity of a few atomic layers is both an advantage and a disadvantage. On the one hand, surfaces can be studied, while, on the other hand, comparison with bulk sensitive techniques is complicated. Photoemission is also a complex many-body process, allowing some uncertainty about the degree to which the standard picture of identifying widths with inverse hole lifetimes is correct. ' To date, there has been very little successful comparison of valence photoemission linewidths and inverse hole lifetimes, some notable failures of this identity, and some controversy. ' ' ' We report here quantitative understanding of the temperature dependence of the linewidth of a Cu(111) surface state based on the phonon contribution to the hole lifetime. In addition, we describe a surface sensitive method of determining one of the most ubiquitous parameters of solid-state physics, P, the electron-phonon mass enhancement parameter.There are three processes that contribute to valence hole decay at zero temperature in metals. One is Auger decay, where one hole decays into two less tightly bound holes and an electron via the electron-electron interaction (electronhole pair creation). The second is phonon scattering, where one hole decays into a less tightly bound hole plus a phonon via the electron-phonon interaction (phonon creation). The third is scattering by an impurity or defect from one momentum to another at fixed energy. At finite temperature,...

Decay of electronic excitations at metal surfaces

“…In this approach the contributions from different phonon modes, in particular the Rayleigh surface mode as well as bulk phonons and the general temperature dependence are taken into account. They also obtain the high temperature behavior represented by l. Their approach is based on: (i) Thomas-Fermi screened Ashcroft electron-ion potentials, (ii) one-electron states obtained from the model potential, and (iii) a simple force-constant phonon model calculation that gives results for the phonon spectrum in good agreement with recently published experimental data [52,86,99,100].…”

“…This fact is also reflected in the absence of a significant peak asymmetry. The authors conclude that the experimental contribution of both Dy and DE to the observed linewidth is 5 meV [99]. However, Fig.…”

“…Except near T ! 0 this broadening can be described approximately [99] by Eq. (40) G ep ¼ 2plk B T, with an experimental value l ¼ 0:14 AE 0:02 for the electron-phonon mass enhancement parameter.…”

“…To improve the angular resolution McDougall et al [99] used very narrow entrance slits, which limit Dy in direction of the surface-state dispersion to Dy ¼ AE0:06 . Their normal emission results are reproduced in Fig.…”

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

“…Thus a measurement of the width of a photoemission peak as a function of temperature provides direct access to the coupling constant, λ. This approach has been used in several studies including a study of the electron-phonon contribution to quasiparticle lifetimes of surface states on the Cu(111) [14] and Be(0001) [15] surfaces. In the former case the electron-phonon coupling constant for the surface, λ = 0.14 was close to that measured for bulk copper, λ = 0.15.…”