Transport coefficients and fluctuations in disordered solids: A field theoretic study

• Main Author: De Souza, Clifford Vincent
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-1991
• Subjects: Condensation; Condensed matter physics
• ISBN: 9798208653036

This thesis looks at the general area of electron behavior in random disordered media in a field theoretic context. Specifically, we investigate the electron conductivity and its fluctuations in regimes characterized by frequency and the absence or presence of electron electron interactions. We initially focus on the non interacting zero frequency conductivity and present a method for its direct calculation by means of a source field formalism. Our results are consistent with previous renormalization group treatments. In view of the interest in universal conductance fluctuations generated by recent experiments and theory, we next calculate within the same formalism, a one loop expression for this. We argue that present field theoretic calculations in the literature are incomplete but find good agreement with a previous diagrammatic perturbation theory calculation. A major inadequacy in the formalism discussed is the absence of a natural variable to prevent infrared divergencies. It is hypothesized that the frequency performs this function. To this end, we extend our formalism to calculate the frequency dependent conductivity and find the expected behaviour. Calculation of conductance fluctuations however reveals a breakdown of this hypothesis. We find that even in the presence of the frequency an infrared divergent term survives. Consequently, we are able to identify three frequency regimes: a low frequency range where fluctuations are universal, an intermediate range in which universality is lost and a high frequency range where universality is regained but at diminished amplitude. Finally, we derive a formalism by which it is possible to directly calculate conductance and conductance fluctuations for disordered interacting electrons. Given the importance of spin phenomena in interacting systems, we focus on both charge and spin transport. With this new formalism, we explicitly calculate both the charge and spin conductivities to lowest nontrivial order in the disorder. Our results for the charge conductivity agree with previous indirect calculations and confirm the Einstein relation. We also calculate charge and spin conductance fluctuations and find the fluctuations of both to be interaction independent and still universal. Higher moments of the conductivities are also found to be interaction independent therefore restricting the possible forms of the conductance distribution functions.