Multiple Plasmon Satellites in Na and Al Spectral Functions fromAb InitioCumulant Expansion

Abstract

The valence photoemission spectra of alkali metals exhibit multiple plasmon satellite structure. The calculated spectral functions within the GW approximation show only one plasmon satellite at too large binding energy. In this Letter we use the cumulant expansion approach to obtain the spectral functions of Na and Al from ab initio calculations including the effects of band structure. The GW spectral functions are dramatically improved and the positions of the multiple plasmon satellites are in very good agreement with experiment while their intensities cannot be explained from intrinsic effects only. [S0031-9007(96)01170-2] PACS numbers: 73.20.Mf, 71.45.Gm, 79.60.Bm The GW approximation (GWA) [1,2] has by now become a standard theory for electronic structure calculations beyond the local density approximation (LDA) [3,4]. It is well known that the GWA well reproduces quasiparticle energies in a wide range of systems from simple systems (simple metals, semiconductors [5,6]) to highly correlated systems (Ni, NiO) [7,8]. There is, however, a problem with the spectral functions in the GWA concerning the satellite structures. It is known, for instance, that the plasmon satellite in the core electron case is positioned too low, 1.5v p (plasmon energy) below the quasiparticle peak rather than v p [9]. Moreover, low energy satellite structures in strongly correlated systems are too weak (or almost missing) and their energies are overestimated [10]. It is clear that a theory beyond the GWA (vertex corrections) is needed to improve the satellite description. An important set of vertex corrections is obtained from the so-called cumulant expansion where one makes a diagrammatic expansion directly in the Green function rather than in the self-energy [11][12][13][14][15]. Previous attempts of including vertex corrections have been mainly concerned with their effects on the quasiparticle energies [16 -18]. As far as we know, the effects of vertex corrections on the satellite structure have not been studied before for real systems.The cumulant expansion has been shown to be very suitable for systems which can be mapped into a polaron Hamiltonian consisting of electrons interacting with bosons (plasmons). Thus, for a core electron interacting with a plasmon field, the first order cumulant expansion already gives the exact result. The physics behind extending this approximation to valence electrons was discussed in detail by Hedin [13]. Two new important developments are, however, made here. References [13,14] dealt with an homogeneous electron gas, while here we treat real systems using a priori band structure calculations based on the linear muffin-tin orbital method [19].While the cumulant expansion has been used to study model systems, applications to real systems are still lacking. For calculational details of the screened interaction and the self-energy, we refer to Refs. [7,20]. The second development is the finding that the satellite contributions to the photoelectron spectrum can be written as a series of terms close...

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