Dynamic response of a strongly perturbed electron gas

Abstract

The theoretical description of many-body systems in their ground state has nowadays become an affordable task because of recent advances in the numerical implementation of ab initio methods, as well as huge improvements in computing capabilities. However, an accurate evaluation of excitedstates properties in such systems is still a major theoretical challenge. The problem is of obvious importance as most experimental techniques are based on testing of excited state. Apart from its intrinsic fundamental interest, the knowledge of the system excitation spectrum is useful to understand a large variety of physical phenomena, such as ~i! photoabsorption of atoms 1,2 and plasmas, 3,4 ~ii! optical response of clusters, 5‐ 8 ~iii! core polarization and dielectric response in solids, 9,10 ~iv! resonant photoemission, 11 or ~v! neutralization of ions at surfaces. 12,13 Common solid-state approaches to study excited states are many-body perturbation and time-dependent densityfunctional theories. The application of these methods to real systems often relies on system symmetries, such as twodimensional or three-dimensional periodicity. The theoretical description of electronic excitations turns out to be more intricate when a localized impurity breaks the spatial symmetry. Numerical methods based on system periodicity are not efficient in this case. Furthermore, localized perturbations in solids, such as impurities in bulk, inner-shell holes, or adsorbates at surfaces strongly modify their environment. The appearance of new states bound to the impurity 14 and/or resonances in the continuum 15 can change dramatically the local properties of the system. The influence of impurity atoms in the excitation spectrum of a 2D electron gas ~where any attractive potential has a bound state! has been considered recently. 16 Kondo-type effects arise for single magnetic impurities as well. 17,18 In metallic systems, valence-band electrons are highly mobile and the presence of an atomic impurity introduces a strong distortion in the electronic density. Our purpose in this work is to show that this rearrangement of electronic charge determines the local dynamic response of the valence electrons to external perturbations. We study the case of an atomic impurity embedded in a free electron gas ~FEG!, which represents the valence band of a simple metal ~such as Na or Al!. Therefore, band-structure effects are not considered as we are interested in determining the local dynamic response of the system. We use density-functional theory to calculate the ground state of the system and obtain the valence-electron response function in linear theory afterwards. We show that the dynamic screening of the Coulomb interaction is highly modified in the vicinity of the impurity and has a complex behavior determined by two competing effects. As an example, we calculate transition probabilities for hole-filling processes in the embedded impurity. We compare some of our results with those obtained in calculations which do not include the presence of the impurity to remark the specific effects introduced by the latter. For small external dynamic perturbations of the system, the many-body response is well described by the linear density response function x(r,r8,v). The self-consistent response function x(r,r8,v) can be obtained at the randomphase approximation ~RPA! level in terms of the response function of a system of independent particles x 0 (r,r8,v) ~atomic units are used throughout unless otherwise stated!: x~ r,r8,v!5x 0 ~ r,r8,v!