Final-state effects in photoemission from filled, narrow bands in metals: A two-level many-electron model.

Abstract

Photoemission from a two-level system interacting with a simple, half-filled conduction band of electrons is considered. The interaction chosen corresponds to final-state, conduction-electron screening of the two localized states from which the two-level system derives. These states are centered on sites spatially separated, and the two-level splitting arises from an assumed intersite tunneling. This tunneling is an extension of the Mahan--Nozieres--de Dominicis--Doniach--S\ifmmode \check{}\else \v{}\fi{}unji\ifmmode \acute{c}\else \'{c}\fi{} model for core-level photoemission to include effects associated with the transfer to an adjacent site of the hole produced by photoexcitation from the two-level system. We compute the photoemission spectra from each of the two levels numerically, using the logarithmic discretization of the conduction band introduced by Wilson for the Kondo problem. The separation between the main peaks in the two spectra is operationally defined to be the two-level separation, in the same way that bandwidths in solids are inferred from angle-resolved photoemission experiments. The splitting is found to be reduced from the ``bare'' splitting appearing in the Hamiltonian, indicating that the conduction-electron screening in the final states narrows the apparent two-level separation. The tunneling of the hole included in this model is also an aspect of photoemission from filled bands in metals, which can be described in terms of a tight-binding, tunneling picture. The question is raised as to whether this effect plays a role in the apparent band narrowing observed in the angle-resolved photoemission spectroscopy of some d-band metals.