Weight of zero-loss electrons and sum rules in extrinsic processes that can influence photoemission spectra K. Schulte, M. A. James, P. G. Steeneken, and G. A. Sawatzky Material Science Center, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands R. Suryanarayanan, G. Dhalenne, and A. Revcolevschi Laboratory de Physico-Chimie de l’e ´tat Solide, CNRS, UMR 8648, Ba ˆt. 414, Universite ´ Paris-Sud, 91405 Orsay, France Received 16 October 2000; published 5 April 2001 It was argued in a recent paper by Joynt Science 284, 777 1999 that in the case of poorly conducting solids a photoemission spectrum close to the Fermi energy may be strongly influenced by extrinsic loss processes similar to those occurring in high-resolution electron-energy-loss spectroscopy, thereby obscuring information concerning the density of states or one-electron Green’s function sought for. In this paper we present a number of arguments, both theoretical and experimental, that demonstrate that energy-loss processes occurring once the electron is outside the solid, contribute only weakly to the spectrum, and can in most cases be either neglected or treated as a weak structureless background. DOI: 10.1103/PhysRevB.63.165429 PACS numbers: 79.60.-i, 82.80.Pv, 75.30.Vn I. INTRODUCTION Photoemission has been used for years as a reliable tech- nique for probing the electronic structure of occupied states in solids ranging from insulators through semiconductors and metals through superconductors. In his paper Joynt 1 provided very convincing and interesting arguments that, especially for badly conducting samples roughly  0 0.1 m cm, the Mott value, the photoelectron spectrum may be affected by energy-loss structures resulting from interaction with the time-dependent fields set up by the photoelectron receding from the surface of the solid. He argued that the influence of these loss processes can be so strong that the spectrum will be dominated by them, and that therefore the intrinsic infor- mation regarding the electronic structure of the solid all but disappears. Since photoemission plays such a prominent role in the discussion of strongly correlated materials like high-T c superconductors, or, more generally, transition-metal oxides, as well as in Kondo and heavy fermion systems, it is of quite some importance to further investigate Joynt’s assertions. In this paper we study Joynt’s arguments, and provide both ex- perimental and theoretical findings that show that the effects due to losses discussed by Joynt are only a small contribu- tion to the total spectrum, and that the zero-energy-loss prob- ability for photoelectrons dominates for samples of either good or bad conductivity. II. INTRINSIC AND PSEUDOINTRINSIC EFFECTS Compared to other techniques, photoemission provides the most easy and direct measurement of the one-electron Green’s function and the directly related occupied density of states of a solid, if one keeps in mind the possible influence on the photoelectron of a number of ‘‘pseudointrinsic’’ effects. 2 By this, we mean, first, the matrix element needed for a description of the amplitude of the optical transition probability from an occupied state to a high-energy unoccu- pied state in the solid; second, the energy-loss processes oc- curring on the electron’s path to the surface; and, finally, the description of the escape of the electron through the surface region into the vacuum. We emphasize that, in the so-called ‘‘sudden approximation,’’ we neglect all interactions and in- terference effects between the high-energy excited electron and the hole left behind. One also has to contemplate truly intrinsic effects: in a one-electron approximation, the associated one-hole Green’s function is a delta peak at an energy determined by the band dispersion of the occupied states. In reality the electrons in the solid are usually not simple free electrons, but interact with other electrons, phonons, magnons, etc., resulting in one-electron Green’s functions now including a frequency- and momentum-dependent self-energy. For weakly interact- ing systems the initial delta function spectrum for such an electron broadens asymmetrically, and attains a frequency distribution for each momentum vector. This basically pro- vides information not only on the quasiparticle dispersion and lifetime, but also on the way the electron is dressed inside the solid, due to the response of its environment to its presence or absence. In strongly interacting systems this self- energy causes a rather large spreading out of the initial delta peaks describing the one-hole Green’s function, and a de- scription in terms of a quasiparticle with a certain lifetime may break down completely. In these cases it is indeed dif- ficult to separate the intrinsic properties of a one-hole Green’s function from pseudointrinsic effects due to the en- ergy losses suffered by the excited electron on its way out of the solid. These losses are basically dominated by the self- energy of the excited electron. It is therefore extremely im- portant to find good estimates of these pseudointrinsic con- tributions to the spectrum, because, in cases where they form a substantial part of the spectrum, one would like to be able to recognize and correct for it and retain only the truly in- trinsic phenomena. Experimentally there are several ways of checking the expected influence of these energy-loss processes. The most obvious is to study the energy-loss spectrum of electrons incident on the solid, with an initial kinetic energy equal to that of the escaping photoelectron. These loss spectra pro- PHYSICAL REVIEW B, VOLUME 63, 165429 0163-1829/2001/6316/1654296/$20.00 ©2001 The American Physical Society 63 165429-1