A heuristic quantum theory of the integer quantum Hall effect

Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the quantum current through a Hall device that does not invoke disorder or interactions as the cause of the integer quantum Hall effect (QHE), but is based on a proper quantization of the classical electron drift motion. The theory yields a quantitative description of the breakdown of the QHE at high current densities that is in agreement with experimental data. Furthermore, several of its key points are in line with recent findings of experiments that address the dependency of the QHE on the 2DEG bias voltage, results that are not easily explained within the framework of conventional QHE models.Comment: 20 pages, 6 figure

Multipolexcitationer i optiska metaatomer

Recent developments in nano-optics and nanofabrication technology have made it possible to construct artificial atoms, called meta-atoms, and out of them compose materials with extraordinary optical properties. These materials are called optical meta-materials. Conventionally, meta-atoms are made of noble metals and have their shapes designed to promote certain types of optically excited electric currents. In this thesis, we develop a multi-pole theory that enables us to exactly identify the excitation character in an arbitrary meta-atom. We propose a new meta-atom design, the disc meta-dimer, and use our multi-pole theory to analyze its properties. In contrast to natural atoms, incident light can interact with this meta-atom without exciting any electric dipole moment. Instead, the light excites pronounced magnetic dipole and electric quadrupole moments. We anticipate that a new type of meta-material, the quadrupole meta-material, can be constructed of these meta-atoms.Den senaste utvecklingen inom nanooptik och nanotillverkning har möjliggjort framställning av artificiella atomer som kallas metaatomer. Utav dem kan man framställa material med enastående optiska egenskaper. Dessa material kallas för optiska metamaterial. Metaatomer är vanligtvis framställda av ädelmetaller och är formade så att de främjar specifika optiskt exciterade elektriska strömmar. I denna avhandling utvecklar vi en multipolteori med vilken vi kan exakt identifiera excitationstypen i en godtycklig metaatom. Vi presenterar skivmetadimern, en ny metaatomdesign vars egenskaper vi analyserar med vår multipolteori. I motsats till naturliga atomer så kan inkommande ljus växelverka med denna metaatom utan att excitera elektriska dipolmoment. Istället exciterar ljuset avsevärda magnetiska dipolmoment och elektriska kvadrupolmoment. Vi förutser att dessa metaatomer kan användas för att framställa en ny typ av metamaterial som vi benämner kvadrupolmetamaterial

Effects of large disorder on the Hofstadter butterfly

Motivated by the recent experiments on periodically modulated, two dimensional electron systems placed in large transversal magnetic fields, we investigate the interplay between the effects of disorder and periodic potentials in the integer quantum Hall regime. In particular, we study the case where disorder is larger than the periodic modulation, but both are small enough that Landau level mixing is negligible. In this limit, the self-consistent Born approximation is inadequate. We carry extensive numerical calculations to understand the relevant physics in the lowest Landau level, such as the spectrum and nature (localized or extended) of the wave functions. Based on our results, we propose a qualitative explanation of the new features uncovered recently in transport measurements.Comment: 15 pages, 13 figures, several pictures have been shrunk to comply with the size requirement

From Wires to Cosmology

We provide a statistical framework for characterizing stochastic particle production in the early universe via a precise correspondence to current conduction in wires with impurities. Our approach is particularly useful when the microphysics is uncertain and the dynamics are complex, but only coarse-grained information is of interest. We study scenarios with multiple interacting fields and derive the evolution of the particle occupation numbers from a Fokker-Planck equation. At late times, the typical occupation numbers grow exponentially which is the analog of Anderson localization for disordered wires. Some statistical features of the occupation numbers show hints of universality in the limit of a large number of interactions and/or a large number of fields. For test cases, excellent agreement is found between our analytic results and numerical simulations.Comment: v3: minor changes and references added; matches published version in JCA

Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric