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Showing 1 to 20 of 58 for “"Quantum Hall effect"”.
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Investigations of the quantum Hall effect in graphene
The purpose of this thesis is to understand the quantum Hall effect in graphene. In particular, we investigate the occurrence of various crystalline phases in the first three Landau levels; we determine which crystalline structure is energetically favorable as the filling factor is varied. In this …
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Microscopic computations in the fractional quantum hall effect
The microscopic picture for fractional quantum Hall effect (FQHE) is difficult to work with analytically for a large number of electrons. Therefore to make predictions and attempt to describe experimental measurements on quantum Hall systems, effective theories are usually employed such as the …
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Imaging transport resonances in the quantum Hall effect
We image charge transport in the quantum Hall effect using a scanning charge accumulation microscope. Applying a DC bias voltage to the tip induces a highly resistive ring-shaped incompressible strip (IS) in a very high mobility 2D electron system (2DES). The IS moves with the tip as it is scanned, …
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Projections and correlations in the fractional quantum Hall effect
… after its surprising experimental discovery, the quantum Hall effect remains one of the most active and interesting fields of research in condensed matter physics. The theory pertaining to the phenomenon comprises a hugely varied and fascinating body of work, incorporating frameworks such as …
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A field theory for the fractional quantum Hall effect
… derive a field theory approach to the Fractional Quantum Hall Effect (FQHE). The goal is to develop a field theory for a system of interacting electrons moving in a plane in the presence of an external magnetic field, in the hope that the FQHE states will appear naturally as the semiclassical …
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Lowest Landau level field theory for the fractional quantum Hall effect
… its relevance to the physics of the fractional quantum Hall effect. For excitation energies much smaller than the cyclotron gap the states can be described in terms of their lowest Landau level content, neglecting the possible mixing between Landau levels induced by the potential terms. The LLL …
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Implementation of the Quantum Hall Effect based precision resistance measurement system
The integer Quantum Hall Effect (QHE) occurs when a two-dimensional electron gas (2DEG) is subjected to a strong perpendicular magnetic field and when the system is cooled to low temperatures. The QHE harbours a wealth of unique phenomena. Of interest is the existence of the Quantum Hall Resistance …
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Laughlin's wave function, plasma analogies and the fractional quantum Hall effect on infinite cylinders
… sowohl fuer die Theorie des fraktionalen Quanten-Hall-Effekts als auch fuer die klassische statische Mechanik geladener Teilchen in einem neutralisierenden Hintergrund von Interesse. Wir zeigen, dass Laughlins Wellenfunktion als Quanten-Polymer-System'' dargestellt werden kann. Die L^2-Norm ist …
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Even denominator quantum numbers and termination of the fractional series in the fractional quantum hall effect
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 1989
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The effects of Landau level mixing, finite thickness, and external electric fields on the $\nu=\frac{5}{2}$ fractional quantum Hall effect
The $\nu=\frac{5}{2}$ fractional quantum Hall effect (FQHE) is a unique and interesting experimental and theoretical state. A great deal of experimental, theoretical and numerical work suggests that this state may support quasihole excitations with non-Abelian statistics, where the order of …
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Entanglement and hall viscosity
This dissertation studies quantum entanglement in relation to the geometric response known as Hall viscosity. We begin by reviewing geometric response in the quantum Hall effect in comparison to its well-known electromagnetic response, Hall conductivity. We develop an understanding of momentum …
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Electron transport in confined structures in very high mobility GaAs in perpendicular magnetic fields
… one focusing on properties in the integer quantum Hall effect the second looking at properties in the fractional quantum Hall effect at filling fraction v = 5/2. Both sets of experiments employ electrostatically defined quantum point contacts (QPCs) fabricated on a high mobility GaAs/AlGaAs …
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Quantum states on spheres in the presence of magnetic fields
The study of quantum states on the surface of various two-dimensional geometries in the presence of strong magnetic fields has proven vital to the theoretical understanding of the quantum Hall effect. In particular, Haldane’s seminal study of quantum states on the surface of a compact geometry, the …
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Single particle spectrum of the two dimensional electron gas
… as those found in the integer and fractional quantum Hall effect, are destroyed by excessive electron heating. Approaches based on tunneling have been hampered by problems such as ohmic heating and low in-plane conductivity, while optical approaches probe long-wavelength excitations which can …
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2D Electron Systems in Undoped GaAs and InGaAs and Progress Towards Undoped GaAs Nano-Structures
… study of novel physical phenomena, such as the Quantum Hall and Fractional Quantum Hall in a 2D electron system (2DES), 1D transport, and single-electron transport in 0D systems. The wide range of systems that can be studied all start with a 2DES from which 1D and 0D systems are formed by …
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Some Topological Aspects of Condensed Matter Physics
… pair. The problem is also studied using an effective Action approach. Edge currents in a quantum spin Hall model in graphene are also studied using similar techniques. A model for the integer quantum Hall effect on a square lattice is presented. Using techniques from algebraic topology, a …
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Quantum Hall transport in graphene and its bilayer
… carriers results in an unconventional integer quantum Hall effect, with a peculiar Landau Level at zero energy. In bilayer graphene, the Dirac-like quadratic energy spectrum leads to an equally interesting, novel integer quantum Hall effect, with a eight-fold degenerate zero energy Landau …
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Exact Diagonalization Studies of Strongly Correlated Systems
… from the Fermi-Hubbard model to the fractional quantum Hall effect (FQHE). The discussion starts with an overview of strongly correlated systems and what is meant by strongly correlated. Then, we extend cluster perturbation theory (CPT), an economic method for computing the momentum and energy …
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Topological phases in narrow-band systems
… through spin-orbit interactions and lattice effects especially narrow-band systems. The first realizes the fractional quantum Hall effect using geometric frustration and ferromagnetism to obtain a nearly flat band with a large bandgap and non-zero Chern number. This system can support this …
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