Theory of Auger-electron and appearance-potential spectroscopy for interacting valence-band electrons.

Abstract

A theory of Auger-electron spectroscopy (AES) and appearance-potential spectroscopy (APS) is presented for interacting electrons in a nondegenerate energy band, described within the framework of the Hubbard model. Both types of spectroscopy are based on the same two-particle spectral density. A diagrammatic vertex-correction method (Matsubara formalism) is used to express this function in terms of the one-particle spectral density. The latter is approximately determined for arbitrary temperature T, arbitrary coupling strength U/W (U, the intra-atomic Coulomb matrix element; W, the width of the ``free'' Bloch band), and arbitrary band occupations n (0\ensuremath{\le}n\ensuremath{\le}2; average number of band electrons per site) by a self-consistent moment method. In weakly coupled systems the electron correlations give rise to certain deformations of the quasiparticle density of states (QDOS) in relation to the Bloch density of states (BDOS), where, however, spontaneous magnetic order is excluded, irrespective of the band filling n.The AE (AP) spectra consist of only one structure a few eV wide (``bandlike'') which is strongly n dependent, but only slightly T dependent, being rather well approximated by a simple self-convolution of the occupied (unoccupied) QDOS. For strongly correlated electrons the Bloch band splits into two quasiparticle subbands. This leads for n1 to one line in the AE spectrum and three lines in the AP spectrum, and vice versa for n>1. For sufficiently strong correlations U/W additional satellites appear that refer to situations where the two excited quasiparticles (quasiholes) propagate as tightly bound pairs through the lattice without being scattered by other charge carriers. As soon as the satellite splits off from the bandlike part of the spectrum, it takes almost the full spectral weight, conveying the impression of an ``atomiclike'' AE (AP) line shape. The satellite has almost exactly the structure of the free BDOS. If the particle density n as well as the hole density 2-n exceed certain critical values determined by U/W and the BDOS ${\mathrm{\ensuremath{\rho}}}_{0}$(E), spontaneous ferromagnetism becomes possible in the strongly correlated electron band. The magnetic phase transition gives rise to a distinctive T dependence for the QDOS and hence also for the AE and AP line shapes. Ferromagnetic saturation, for example, may lead to complete suppression of certain parts of the spectra. From integrated AE and AP intensities one can read off the full temperature behavior of density-density and spin-spin correlation functions. The simple self-convolution model for the two-particle spectral density turns out to be inappropriate for highly correlated electron systems.