Inelastic electron and light scattering from the elementary electronic excitations in quantum wells: Zero magnetic field

TL;DR

This paper develops a comprehensive theoretical framework for inelastic electron and light scattering in GaAs/Ga$_{1-x}$Al$_{x}$As quantum wells, analyzing electronic excitations and their experimental signatures.

Contribution

It introduces a systematic derivation of the dielectric functions and scattering theories applicable to quantum wells, including analytical solutions for various excitation spectra and scattering geometries.

Findings

Computed excitation spectra including intrasubband and intersubband modes

Derived loss functions for different scattering geometries

Calculated Raman intensities indicating real electronic transitions

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/Ga$_{1-x}$Al$_{x}$As 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...