This dissertation is devoted to theoretical studies of strongly interacting one-dimensional and quasi one-dimensional electron systems. The properties of one-dimensional electron systems can be studied within the bosonization technique, which presents fermions as collective bosonic density excitations. The power of this approach is the ability to treat electron-electron interaction exactly in the low-energy limit. The approach predicts the failure of Fermi liquid and an absence of long-range order in one-dimensions. The low-energy description of one-dimensional interacting systems is called the Tomonaga-Luttinger liquid theory. For example, the edges of quantum Hall systems are one-dimensional and described by a chiral Tomonaga-Luttinger liquid. Another example is a quantum spin Hall system with helical edge states, which are also described by a Tomonaga-Luttinger liquid. In our first work, a study of magnetized edge states of quantum spin-Hall system is presented. A magnetic field dependent signature of such edges is obtained, which can be verified in a Coulomb drag experiment. The second part of the dissertation is devoted to quasi-one dimensional antiferromagnetic lattices. A spatially anisotropic lattice antiferromagnet can be viewed as an array of one dimensional spin chains coupled in a way to match the lattice symmetry. This allows to use the non-Abelian bosonization technique to describe the low-energy physics of spin chains and study the inter-chain interactions perturbatively. The work presented in the dissertation studies the effect of Dzyaloshinskii-Moriya interaction on the magnetic phase diagram of the spatially anisotropic kagome antiferromagnet. We predict a Dzyaloshinskii-Moriya interaction driven phase transition from Neel to Neel+dimer state. In the third work, a novel model of the fractional quantum Hall effect is given. Wave functions of two-dimensional electrons in strong and quantizing magnetic field are essentially one-dimensional. That invites one to use the one-dimensional phenomenological bosonization to describe the density fluctuations of the two-dimensional interacting electrons in magnetic field. Remarkably, the constructed trial bosonized fermion operator describing the electron states with a fixed Landau gauge momentum is effectively two-dimensional. / text

In this thesis we discuss quantum Hall effects in bilayer graphene and other novel two-dimensional electron systems, focusing on the interplay between nontrivial Fermi surface topology and electron-electron interactions. In the first chapter I will give a brief introduction to some aspects of the quantum Hall effects. The second chapter discusses the physics in bilayer graphene in the absence of external magnetic fields. The first half discusses the band gap opening and trigonal warping effects in its bandstructure, and the second half focuses on the insulating ground state that results from electron-electron interactions. The third chapter discusses the single-particle Landau level structure in bilayer graphene. We will see that when both the band gap and trigonal warping effects are present, the highest Landau level in the valence band is three-fold degenerate at small magnetic fields. As the field increases, the three fold degeneracy is lifted and the Landau level structure gradually reduces to that in the absence of trigonal warping effects. At the end of the chapter we will demonstrate a formalism to map the momentum distribution of the single-particle Landau level structure. Such a mapping will give valuable information about the single-particle bandstructure. The fourth chapter deals with electron-electron interactions in the integer quantum Hall regime, where there is no fractional filling of the orbital degrees of freedom. In such a regime, the effect of electron-electron interactions often leads to spontaneous ordering of the internal degrees of freedom, such as spin, layer and valley. The first part of the chapter will establish the general formalism of Hartree-Fock theory in the quantum Hall regime, and then a specific theory for gapped bilayer graphene with trigonal warping effects is constructed. The resulting ground states are analyzed in the last part of the chapter. / text

No description available.

Detailed magnetometry and polarized neutron reflectometry studies were conducted on MnSi thin films grown epitaxially on Si(111) substrates. It is demonstrated that with an in-plane applied field H || [110], a broadly stable skyrmion phase exists at elevated temperatures and fields. Magnetometry and transport measurements with an out-of-plane applied field H || [111] prove that no skyrmion phase exists in this geometry. However, Hall effect measurements in this geometry show unexpected evidence of a topological Hall effect. This can be explained with a multi-dimensionally modulated cone phase, which proves that contrary to recent literature, a topological Hall effect is not sufficient proof of skyrmions. The results of this thesis represent a significant step towards a technologically relevant material in which skyrmions are broadly stable. A material of this type could be used in novel magnetic storage devices and signi ficantly impact our future computing capabilities.

In this thesis, I present the work performed towards a proposal to couple a piezoelectric, nanomechanical beam to a radio frequency single electron transistor (RF-SET). Lumped element RF circuit theory is applied to 50 kOhm single electron transistors acting as the resistor in an RLC circuit. It is shown that for the expected inductances and stray capacitances, at an operating frequency of 1.25 GHz, the RF-SET is expected to have a usable half-bandwidth of 175-200 MHz and a charge sensitivity on the order of 10^(−5) e/√Hz. A fabricated RF-SET device is cryogenically cooled and used to find experimental values of the stray capacitance. A heterostructure made of gallium arsenide and aluminum gallium arsenide from which piezoelectric beams can be made is designed to contain a 2-dimensional electron gas (2DEG). Quantum Hall effect samples are fabricated from the wafer, and magnetoresistance measurements for each sample are presented. It is shown that the 2DEG has a high electron concentration of about 8 × 10^11 cm−2 but a low mobility of about 3.5 × 10^4 cm^2/(V·s) for this type of heterostructure. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2010-03-01 22:55:56.427

The first part of this thesis is a study of thermally activated conduction, Hall effect, and Far-Infrared absorption in n-InP. Accurate measurements of threshold energies are deduced from the temperature dependence of these effects, after correction for Fermi level variations, and it is shown that the threshold for electrical conduction is higher than for Hall effect, or cyclotron resonance. An explanation is given in terms of the long range impurity potential fluctuations. The second part of this thesis presents measurements of the thermopower in heterostructures for the GaInAs - InP, GaInAs - InAlAs, and GaAs - GaAlAs systems, with and without magnetic field, for temperature varying from 2K to 10K. In high magnetic fields, strong oscillations of the thermopower are seen, with the same phase as the Shubnikov - de Haas oscillations in the resistivity, in accordance with theory. The magnitude and temperature dependence of the thermopower are mostly as predicted for the superlattice but those of the heterojunctions disagree with the predictions. A discussion of the cause of this disagreement is given. In the final part, the value of the relative energy shift between different valleys of the conduction band of a thin film of PbTe grown on BaF₂ is obtained. This will be used to obtain the deformation potential of PbTe.

Thesis (M.Sc.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2008/12/04). Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains ix, 161 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 152-158).

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [108]-114).

Thesis (Ph. D.)--Rutgers University, 2007. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 134-138).