The fractional quantum Hall effect (FQHE), now entering it's fourth decade, continues to draw attention from the condensed matter community. New experiments in recent years are raising hopes that it will be possible to observe quasi-particles with non-abelian anyonic statistics. These particles could form the building blocks of a quantum computer. The quantum Hall states have topologically protected energy gaps to the low-lying set of excitations. This topological order is not a locally measurable quantity but rather a non-local object, and it is one of the keys to it's stability. From an early stage understanding of the FQHE has been facilitate by constructing trial wave functions. The topological classification of these wave functions have given further insight to the nature of the FQHE. An early, and successful, wave function construction for filling fractions ν=p/(2p+1) was that of composite fermions on planar and spherical geometries. Recently, new developments using conformal field theory have made it possible to also construct the full Haldane-Halperin hierarchy wave functions on planar and spherical geometries. In this thesis we extend this construction to a toroidal geometry, i.e. a flat surface with periodic boundary conditions. One of the defining features of topological states of matter in two dimensions is that the ground state is not unique on surfaces with non trivial topology, such as a torus. The archetypical example is the fractional quantum Hall effect, where a state at filling fraction ν=p/q, has at least a q-fold degeneracy on a torus. This has been shown explicitly for a few cases, such as the Laughlin states and the the Moore-Read states, by explicit construction of candidate electron wave functions with good overlap with numerically found states. In this thesis, we construct explicit torus wave functions for a large class of experimentally important quantum liquids, namely the chiral hierarchy states in the lowest Landau level. These states, which includes the prominently observed positive Jain sequence at filling fractions ν=p/(2p+1), are characterized by having boundary modes with only one chirality. Our construction relies heavily on previous work that expressed the hierarchy wave functions on a plane or a sphere in terms of correlation functions in a conformal field theory. This construction can be taken over to the torus when care is taken to ensure correct behaviour under the modular transformations that leave the geometry of the torus unchanged. Our construction solves the long standing problem of engineering torus wave functions for multi-component many-body states. Since the resulting expressions are rather complicated, we have carefully compared the simplest example, that of ν=2/5, with numerically found wave functions. We have found an extremely good overlap for arbitrary values of the modular parameter τ, that describes the geometry of the torus. Having explicit torus wave functions allows us to use the methods developed by Read and Read \&amp; Rezayi to numerically compute the quantum Hall viscosity. Hall viscosity is conjectured to be a topologically protected macroscopic transport coefficient characterizing the quantum Hall state. It is related to the shift of the same QH-fluid when it is put on a sphere. The good agreement with the theoretical prediction for the 2/5 state strongly suggests that our wave functions encodes all relevant topologically information. We also consider the Hall viscosity in the limit of a very thin torus. There we find that the viscosity changes as we approach the thin torus limit. Because of this we study the Laughlin state in that limit and see how the change in viscosity arises from a change in the Hamiltonian hopping elements. Finally we conclude that there are both qualitative and quantitative difference between the thin and the square torus. Thus, one has to be careful when interpreting results in the thin torus limit. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.</p>

No description available.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [85]-95).

Thesis (Ph. D.)--Cornell University, 1915. / "Reprinted from the Physical review, second series, vol. 7, no. 2, February, 1916."

Thesis (Ph.D.)--Pennsylvania State University, 2009. / Mode of access: World Wide Web. Thesis advisor: Jainendra K. Jain.

Thesis (M.S.)--University of Wisconsin--Madison, 1961. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 52).

Thesis (M.S.)--University of Wisconsin--Madison, 1962. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 70).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Allan H. MacDonald. Vita. Includes bibliographical references.

A series of as-grown ZnO layers have been electrically characterised by the temperature dependent (20 – 300 K) Hall-effect technique. The ZnO layers were grown by metal organic chemical vapour deposition (MOCVD) on glass substrates under various growth conditions. The temperature dependent Hall-effect technique produced mobility and carrier concentration measurements. These measurements were found to be reproducible and reliable. The carrier concentration data for the layers was fitted by the charge balance equation to accurately determine the donor level and corresponding donor concentration as well as the acceptor concentration for each sample. The measured donor levels were found to vary from sample to sample and there is evidence from the results that the variations are related to the differing growth conditions of the layers. The mobility data was also fitted to establish the dominant electron scattering mechanisms in the layers. The dominant scattering mechanisms were found to vary from sample to sample. For most of the layers studied, the dominant scattering mechanism was found to be both the ionised impurity scattering at low temperatures (20 – 100 K) and grain boundary scattering at higher temperatures (100 – 300 K). The effects of exposing the ZnO layers to hydrogen plasma were also investigated by the temperature dependent Hall-effect technique. Findings indicate that hydrogen is readily incorporated in ZnO, leading always to an increased carrier concentration. It was further noted that incorporating hydrogen into ZnO in some layers increased the mobility while in other layers it caused a decrease in the mobility. The hydrogenated samples were subsequently annealed at 600 °C for 1 hour in argon ambient resulting in the carrier concentration reducing to its original value. This effect is attributed to hydrogen diffusing out of ZnO.

No description available.