Electron energy-loss and photoelectron spectroscopies of surfaces and two-dimensional crystals

Dielectric response of crystal surfaces and quasi two-dimensional (Q2-Dquasi two-dimensional (Q2-D)) crystals to incident electrons and photons underlies a variety of electronic and optical phenomena, such as the excitation of monopole, multipole, two-dimensional (2-D), and acoustic plasmons, which have vast implications for optical and electron spectroscopies. This chapter covers model and electronic structure approaches to dynamic dielectric screening and discusses the development of the field from the pioneering works by R.H. Ritchie and P. Feibelman up to recent ab-initio developments. Starting with the quantum-mechanical expression for the microscopic dielectric response (Sect. 17.1), we explain the emergence of surface plasmon modes and discuss their structure based on simplified model systems. We further introduce an ab-initio approach to calculate the response function for realistic systems. We discuss how the excitations manifest themselves in the inelastic scattering of electrons reflected from a solid surface or a Q2"​ D crystal (Sect. 17.2), at first confining ourselves to the conventional formalism of energy-loss functions. We then demonstrate the necessity to go beyond this formalism and present the theory of the inelastic scattering of electrons, which takes into account the effect of the kinematics of the probing particle on the excitation process (Sect. 17.3). Finally, we show how the nonlocal response to the incident light leads to a strong enhancement of the microscopic electric field at the surface and how the total exciting field can be included into an ab-initio one-step photoemission theory to describe photoyield enhancement (Sects. 17.6 and 17.7).