Correlation-Induced Double-Plasmon Excitation in Simple Metals Studied by Inelastic X-Ray Scattering

Abstract

We report a new type of peaklike structure observed in the tail of the dynamic structure factor of simple metals, measured by inelastic x-ray scattering. Based on the momentum-transfer dependence of the energy position and the intensity of this structure, it has been unambiguously attributed to intrinsic plasmonplasmon excitations, an electronic correlation effect that was theoretically predicted by many-body perturbation theory of the homogeneous-electron-gas model beyond the random-phase approximation. This signature appears to be largely unaffected by electron-ion interaction effects. Thus a structure that is primarily caused by correlation effects in the electron gas has been found experimentally in the dynamic structure factor of simple metals. DOI: 10.1103/PhysRevLett.95.157401 PACS numbers: 78.70.Ck, 71.10.Ca, 71.45.2d The appropriate theoretical treatment of correlation in an interacting electron gas at metallic densities still remains a challenge in spite of the large amount of work on this topic. Therefore, experimental methods that can directly test theoretical predictions are very valuable. For systems that closely resemble a homogeneous electron gas (jellium), measurements of the dynamic structure factor S q; ! as a function of the momentum transfer q and the energy loss ! offer such a testing ground of correlation effects, since S q; ! is the Fourier transform in space and time of the density-density correlation function [1]. Inelastic x-ray scattering (IXS) is the favorable experimental method to study S q; ! for large momentum transfers q [2], i.e., when short-range correlations are probed. In particular, the advantage of IXS is the nearly complete absence of multiple scattering in contrast to electron energy-loss spectroscopy (EELS) [3], because in EELS extrinsic multiple excitations can obscure the information on electron correlations. IXS studies on simple metals [4] clearly showed significant deviations of the overall shape of S q; ! for large q from the shape predicted by the jellium model in the random-phase approximation (RPA) [5]. The RPA is known to incorporate long-range correlations only and thus for small q jqj approximately accounts for the energy position and dispersion of collective excitations such as plasmons in simple metals. In both cases the influence of the effective electron-ion interaction is found to be small. For larger q the deviations of the experimental observations from the RPA jellium calculations exhibit three characteristic features: (i) the centroid of S q; ! as a function of ! is shifted to lower energy losses [4]; (ii) a double-peak or a one-peak-one-shoulder structure appears to be universal for all simple metals [5]; (iii) the S q; ! spectra show tails for ! far beyond the upper limit of the jellium (single) particle-hole excitation spectrum [6,7].All three observed features were attributed to correlation effects beyond the RPA [4,[8][9][10][11][12][13]. However, the ion potential was found to cause similar effects [13][14][15][16][17][18]. As a result, it...

Electron-density dependence of double-plasmon excitations in simple metals

“…The results for Al have been pub- lished earlier and are reproduced here for comparison. 22 All spectra are dominated by a single peak around the plasmon energy pl ͑q͒. In all cases, there is also a small shoulder roughly at 2 pl ͑q͒, which disperses and broadens with an increasing momentum transfer.…”

“…3 to S͑q , ͒, as far as double-plasmon excitations are concerned. However, contrary to the C diagrams, 22 we find that the RPA screening yields, after integration over two internal energy variables, in all cases, products of the form…”

“…Part of the results for Al have been published earlier. 22 The Al samples were 0.4 mm thick single crystals aligned so that it was possible to measure the energy-loss spectra with the momentum transfer vector parallel to the ͓110͔ and ͓100͔ directions. The Mg sample was a 0.7 mm thick polycrystalline pellet.…”

“…Note that the pl-pl peak in Im͓ C pl-pl ͑q , ͔͒ is the result of integrating pl-pl excitations over the internal energy and momentum variables. 22 Fit FIG. 1.…”

“…Indeed, the existence of the pl-pl excitations in Al has recently been clearly demonstrated to be in very good agreement with the theory. 22 The double-plasmon excitations have also been sought for by EELS studies. 23,24 In EELS, the extrinsic multiplescattering events overlap with the pl-pl excitations and their contribution has to be extracted based on the estimates of multiple-scattering probability, which can make the analysis difficult.…”