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Register a new userMany-body calculations of plasmon and phonon satellites in angle-resolved photoelectron spectra using the cumulant expansion approach
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The interaction of electrons with crystal lattice vibrations (phonons) and collective charge-density fluctuations (plasmons) influences profoundly the spectral properties of solids revealed by photoemission spectroscopy experiments. Photoemission satellites, for instance, are a prototypical example of quantum emergent behavior that may result from the strong coupling of electronic states to plasmons and phonons. The existence of these spectral features has been verified over energy scales spanning several orders of magnitude (from 50 meV to 15-20 eV) and for a broad class of compounds such as simple metals, semiconductors, and highly-doped oxides. During the past few years the cumulant expansion approach, alongside with the GW approximation and the theory of electron-phonon and electron-plasmon coupling in solids, has evolved into a predictive and quantitatively accurate approach for the description of the spectral signatures of electron-boson coupling entirely from first principles, and it has thus become the state-of-the-art theoretical tool for the description of these phenomena. In this chapter we introduce the fundamental concepts needed to interpret plasmon and phonon satellites in photoelectron spectra, and we review recent progress on first-principles calculations of these features using the cumulant expansion method.
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We develop a first-principles approach based on many-body perturbation theory to investigate the effects of the interaction between electrons and carrier plasmons on the electronic properties of highly-doped semiconductors and oxides. Through the evaluation of the electron self-energy, we account simultaneously for electron-plasmon and electron-phonon coupling in theoretical calculations of angle-resolved photoemission spectra, electron linewidths, and relaxation times. We apply this methodology to electron-doped anatase TiO2 as an illustrative example. The simulated spectra indicate that electron-plasmon coupling in TiO2 underpins the formation of satellites at energies comparable to those of polaronic spectral features. At variance with phonons, however, the energy of plasmons and their spectral fingerprints depends strongly on the carrier concentration, revealing a complex interplay between plasmon and phonon satellites. The electron-plasmon interaction accounts for approximately 40% of the total electron-boson interaction strength and it is key to improve the agreement with measured quasiparticle spectra.
We have studied the O 2p valence-band structure of Nb-doped SrTiO3, in which a dilute concentration of electrons are doped into the d0 band insulator, by angle-resolved photoemission spectroscopy (ARPES) measurements. We found that ARPES spectra at the valence band maxima at the M [k = (pi/a, pi/a, 0)]and R [k = (pi/a, pi/a, pi/a)] points start from ~ 3.3 eV below the Fermi level (EF), consistent with the indirect band gap of 3.3 eV and the EF position at the bottom of the conduction band. The peak position of the ARPES spectra were, however, shifted toward higher binding energies by ~ 500 meV from the 3.3 eV threshold. Because the bands at M and R have pure O 2p character, we attribute this ~ 500 meV shift to strong coupling of the oxygen p hole with optical phonons in analogy with the peak shifts observed for d-electron photoemission spectra in various transition-metal oxides.
In this work the complete valence-band structure of the molybdenum dichalcogenides MoS_2, MoSe_2, and alpha-MoTe_2 is presented and discussed in comparison. The valence bands have been studied using both angle-resolved photoelectron spectroscopy (ARPES) with synchrotron radiation, as well as, ab-initio band-structure calculations. The ARPES measurements have been carried out in the constant-final-state (CFS) mode. The results of the calculations show in general very good agreement with the experimentally determined valence-band structures allowing for a clear identification of the observed features. The dispersion of the valence bands as a function of the perpendicular component k_perp of the wave vector reveals a decreasing three-dimensional character from MoS_2 to alpha-MoTe_2 which is attributed to an increasing interlayer distance in the three compounds. The effect of this k_perp dispersion on the determination of the exact dispersion of the individual states as a function of k_parallel is discussed. By performing ARPES in the CFS mode the k_parallel-component for off-normal emission spectra can be determined. The corresponding k_perp-value is obtained from the symmetry of the spectra along the GammaA, KH, and ML line, respectively.
We present ab initio calculations of the photoemission spectra of bulk sodium using different flavors of the cumulant expansion approximation for the Greens function. In particular, we study the dispersion and intensity of the plasmon satellites. We show that the satellite spectrum is much more sensitive to many details than the quasi-particle (QP) spectrum, which suggests that the experimental investigation of satellites could yield additional information beyond the usual studies of the band structure. In particular, a comparison to the homogeneous electron gas (HEG) shows that the satellites are influenced by the crystal environment, although the crystal potential in sodium is weak. Moreover, the temperature dependence of the lattice constant is reflected in the position of the satellites. Details of the screening also play an important role; in particular, the contribution of transitions from 2s and 2p semi-core levels influence the satellites, but not the QP. Moreover, inclusion of contributions to the screening beyond the RPA has an effect on the satellites. Finally, we elucidate the importance of the coupling of electrons and holes by comparing the results of the time-ordered (TOC) and the retarded (RC) cumulant expansion approximations. Again, we find small but noticeable differences. Since all the small effects add up, our most advanced calculation yields a satellite position which is improved with respect to previous calculations by almost one eV. This stresses the fact that the calculation of satellites is much more delicate than the calculation of a QP band structure.
We describe an approach for calculations of phonon contributions to the electron spectral function, including both quasiparticle properties and satellites. The method is based on a cumulant expansion for the retarded one-electron Greens function and a many-pole model for the electron self-energy. The electron-phonon couplings are calculated from the Eliashberg functions, and the phonon density of states is obtained from a Lanczos representation of the phonon Greens function. Our calculations incorporate ab initio dynamical matrices and electron-phonon couplings from the density functional theory code ABINIT. Illustrative results are presented for several elemental metals and for Einstein and Debye models with a range of coupling constants. These are compared with experiment and other theoretical models. Estimates of corrections to Migdals theorem are obtained by comparing with leading order contributions to the self-energy, and are found to be significant only for large electron-phonon couplings at low temperatures.
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