Localisation and interactions in disordered electron systems
Localisation and interactions in disordered electron systems
The outstanding feature of disordered systems is that their single-particle eigenstates exhibit a transition from being extended throughout the system to being localised in part of it. In our thesis, we are concerned with this localisation transition and the effects of Coulomb interactions on eigenstates at or near the transition point. Chapter One contains a general discussion of the relevant aspects of disordered systems with which we deal in subsequent chapters. In Chapter Two, we study localisation using a model for wave propagation on a Cayley tree. Our model contains simplifying features which allow us to solve extensively using elementary methods. We find a rich variety of behaviour, specific to the Cayley tree, which has previously not been much emphasised. In Chapter Three, we examine screening and inelastic scattering in a disordered system in which electronic diffusion is novel in the sense that it is characterised by a wavevector- and frequency-dependent diffusion coefficient. In particular, we calculate the temperature dependence of the quasielectron scattering rate. We discuss the result of our calculation in the context of known theoretical and experimental data and point out some apparent contradictions which need to be resolved. In Chapter Four, we investigate the consequences of including Coulomb interactions into a model for the quantum Hall effect which contains slowly varying random potential. We concentrate on screening and, via simple arguments, find that Coulomb interactions do not cause any significant changes in the model.
University of Southampton
1989
Siak, Selina Chin Yoke
(1989)
Localisation and interactions in disordered electron systems.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
The outstanding feature of disordered systems is that their single-particle eigenstates exhibit a transition from being extended throughout the system to being localised in part of it. In our thesis, we are concerned with this localisation transition and the effects of Coulomb interactions on eigenstates at or near the transition point. Chapter One contains a general discussion of the relevant aspects of disordered systems with which we deal in subsequent chapters. In Chapter Two, we study localisation using a model for wave propagation on a Cayley tree. Our model contains simplifying features which allow us to solve extensively using elementary methods. We find a rich variety of behaviour, specific to the Cayley tree, which has previously not been much emphasised. In Chapter Three, we examine screening and inelastic scattering in a disordered system in which electronic diffusion is novel in the sense that it is characterised by a wavevector- and frequency-dependent diffusion coefficient. In particular, we calculate the temperature dependence of the quasielectron scattering rate. We discuss the result of our calculation in the context of known theoretical and experimental data and point out some apparent contradictions which need to be resolved. In Chapter Four, we investigate the consequences of including Coulomb interactions into a model for the quantum Hall effect which contains slowly varying random potential. We concentrate on screening and, via simple arguments, find that Coulomb interactions do not cause any significant changes in the model.
This record has no associated files available for download.
More information
Published date: 1989
Identifiers
Local EPrints ID: 458260
URI: http://eprints.soton.ac.uk/id/eprint/458260
PURE UUID: 4699f796-325c-4203-801b-906b39b7b918
Catalogue record
Date deposited: 04 Jul 2022 16:45
Last modified: 04 Jul 2022 16:45
Export record
Contributors
Author:
Selina Chin Yoke Siak
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics