Εντοπισμός και γραμμική απόκριση ηλεκτρονίων στο άτακτο πλέγμα

The study of the localization, and transport properties in disordered systems is considered to be a hard theoretical problem. The localization problem has been given considerable attention in the literature while the transport one has rarely been studied in depth, because it constitutes an even harder quantum mechanical problem. In the present thesis we developed for the first time a method of exact calculation of the localization and transport properties of non-interacting electrons in disordered systems, based on the calculation of probability distributions of variables properly derived from the Green's function of the problem. Such a calculation became feasible when we considered our system to obey a tight binding model with diagonal disorder and furthermore that its lattice sites form a Bethe lattice. The special Bethe lattice topology allows for the calculation of the necessary probability distributions through closed integral expressions. Using these probability distributions we calculated the exact localization and diffusion properties and the mobility edges more specifically which we compared with approximate results given in the literature. In studying the transport properties we succeeded to express the electrical response through factors representing the "local" response of the various parts of our system to external potential gradients applied "locally" too. The use of such expressions involving "local" conductances gives us a great advantage by allowing for the calculation of their statistical behavior through the probability distributions mentioned above. We investigate likewise the conductivity properties thoroughly and from various points of view, since it is a very important field in which few exact results exist, especially as far as the microstructure of the system dynamic response is concerned. We thus study the "local" conductance as a function of the frequency ω, for EF in (i) the localized and (ii) the extended states part of the energy spectrum and we focus mainly in the small ω regime. All respective results reveal the possibility of this quantity to bring about the response properties of the system at the microscopic level. We conclude our thesis with a critical review and a discussion of the present and prospective achievements of the work.

Grantor dc:publisher

National Technical University of Athens (NTUA)

Year dc:date

1990

Authors dc:creator

• Kleanthous, Kleanthis
• Κλεάνθους, Κλεάνθης

• Αγωγιμότητα
• Άτακτα
• Γραμμική απόκριση
• Ειδική αγωγιμότητα
• Εντοπισμός
• Όρια ευκινησίας
• ΠΛΕΓΜΑ ΒΕΤΗΕ
• Bethe lattice
• Conductance
• Contuctivity
• Disorder
• Linear response
• Localization
• Mobility edges
• Φυσικές Επιστήμες
• Φυσική
• Natural Sciences
• Physical Sciences

Language dc:language

gre

Identifier

10.12681/eadd/1371

OAI identifier oai:identifier

oai:10442/1371