Micklitz, Tobias (2006) Application of field theoretical methods to problems in mesoscopic physics. PhD thesis, Universität zu Köln.
The subject of this thesis are three different topics related to quantum interference and dephasing in weakly disordered mesoscopic systems. The first topic covers the so-called ``current echo", which is a quantum-interference phenomenon predicted about a decade ago by Thomas et al. on the basis of numerical calculations. Our motivation to study the current echo originates from the fact that a simple physical picture explaining its appearance so far has been missing. It is shown that all characteristic features of Thomas' current echo can be explained resorting to the well known phenomenon of weak localization in disordered systems. In view of recent technological progress in the creation of voltage pulses on a pico-second time scale, the experimental verification of the current echo should be feasible. The echo phenomenon may become a useful tool to determine dephasing rates in weakly disordered systems. The second topic is titled ``Dephasing by Kondo impurities". In this part of the thesis we derive an analytical expression for the dephasing rate of non-interacting electrons propagating in a weakly disordered environment and scattering from very low concentrations of magnetic impurities. The motivation to study dephasing due to Kondo impurities traces back to a series of experiments performed over the last decade which show an unexpected saturation of the dephasing rate at lowest temperatures. The observed saturation clearly deviates from theoretical predictions based on the assumption that inelastic scattering due to electron-electron interactions is the dominant mechanism for dephasing. Therefore, it was suggested, that inelastic scattering from low concentrations of magnetic impurities may be responsible for the observed excess of dephasing. So far these speculations could not be quantitatively tested, since the dephasing rate due to diluted magnetic impurities in the experimentally probed range of temperature was unknown. Based on our results a quantitative comparison between theoretically predicted and experimentally measured dephasing rate was done. This allowed for a critical examination of the relevance of low concentrations of magnetic impurities for the observed behaviour of the dephasing rate. Moreover, this part of the thesis analyzes the magnetic field dependence of the dephasing rate due to magnetic impurities and generalizes the results for the dephasing rate from magnetic to arbitrary diluted dynamical impurities. The third topic of this thesis relates to quantum interference and dephasing in a disordered Luttinger liquid. The standard approach to describe interacting one-dimensional systems is the bosonization method, which, however, becomes very intransparent when in addition disorder comes into play. Therefore, quantum interference phenomena and dephasing in a disordered Luttinger liquid remained unaddressed for a long time. In this part of the thesis we follow a new road and derive an effective field theory for the disordered Luttinger liquid. This model allows to systematically explore interference phenomena in disordered Luttinger liquids. As an application of the model we discuss for the first time the persistent current in a weakly disordered Luttinger liquid.
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