Abstract
The most fundamental approach to an understanding of electronic, optical, and transport phenomena which the condensed matter physics (of conventional as well as nonconventional systems) offers is generally founded on two experiments: the inelastic electron scattering and the inelastic light scattering. This work embarks on providing a systematic framework for the theory of inelastic electron scattering and of inelastic light scattering from the electronic excitations in GaAs/Ga1−xAlxAs quantum wells. To this end, we start with the Kubo's correlation function to derive the generalized nonlocal, dynamic dielectric function, and the inverse dielectric function within the framework of Bohm-Pines’ random-phase approximation. This is followed by a thorough development of the theory of inelastic electron scattering and of inelastic light scattering. The methodological part is then subjected to the analytical diagnoses which allow us to sense the subtlety of the analytical results and the importance of their applications. The general analytical results, which know no bounds regarding, e.g., the subband occupancy, are then specified so as to make them applicable to practicality. After trying and testing the eigenfunctions, we compute the density of states, the Fermi energy, the full excitation spectrum made up of intrasubband and intersubband – single-particle and collective (plasmon) – excitations, the loss functions for all the principal geometries envisioned for the inelastic electron scattering, and the Raman intensity, which provides a measure of the real transitions induced by the (laser) probe, for the inelastic light scattering. It is found that the dominant contribution to both the loss peaks and the Raman peaks comes from the collective (plasmon) excitations. As to the single-particle peaks, the analysis indicates a long-lasting lack of quantitative comparison between theory and experiments. It is inferred that the inelastic electron scattering can be a potential alternative of the inelastic light scattering for investigating elementary electronic excitations in quantum wells.
Highlights
Scientific advances in any field are generally known to have been advocated on the basis of a sound competition between the theory and the experiment
This obviously necessitates a systematic knowledge of the single-particle and collective excitation spectrum, at least, for the sake of comparing and justifying the loss peaks in the inelastic electron scattering (IES) and the intensity peaks in the inelastic light scattering (ILS)
II, we present the theoretical framework leading to the derivation of nonlocal, dynamic, dielectric function, screened potential, inverse dielectric function, Dyson equation, probability function characterizing the inelastic electron scattering, and the cross-section for inelastic light scattering
Summary
Scientific advances in any field are generally known to have been advocated on the basis of a sound competition between the theory and the experiment. The purpose of the present paper is to develop a comprehensive theory of the inelastic electron and inelastic light scattering in the single quantum wells in the absence of any applied magnetic field This obviously necessitates a systematic knowledge of the single-particle and collective (plasmon) excitation spectrum, at least, for the sake of comparing and justifying the loss peaks in the IES and the intensity peaks in the ILS. To this end, we derive the required nonlocal, dynamic dielectric function, inverse dielectric function, and other correlation functions in the framework of Bohm-Pines’ full random-phase approximation (RPA) [62]. IV, we conclude our finding and suggest some interesting features worth adding to the problem
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