Luttinger Liquid Behavior in Low-Dimensional Systems
Sandler, Nancy Patricia
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https://hdl.handle.net/2142/30856
Description
Title
Luttinger Liquid Behavior in Low-Dimensional Systems
Author(s)
Sandler, Nancy Patricia
Issue Date
1998-08
Director of Research (if dissertation) or Advisor (if thesis)
Fradkin, Eduardo H.
Doctoral Committee Chair(s)
Stine, M.
Committee Member(s)
Klein, Miles V.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Luttinger liquids (LL)
low-dimensional electronic systems
quantum wires
fractional quantum Hall effect
Language
en
Abstract
The purpose of this thesis is the study of different low-dimensional systems displaying the physical properties of Luttinger liquids (LL). In recent years, the LL model has been succesfully applied to understand the transport properties, and recently noise measurements, of low-dimensional electronic systems. In this thesis, I focus on quantum wires (QW) and two-dimensional systems exhibiting the fractional quantum Hall effect (FQHE) as two different examples of systems showing Luttinger liquid behavior. In the case of QW, I analyze the effect of the dimensionality crossover on the finite temperature conductance in weakly disordered quantum wires. I show that although the quasi-one-dimensional QW exhibits a typical Luttinger liquid behavior for a small number of channels in the wire, the well-established Fermi liquid picture sets in when the number of channels increases. As another example of LL behavior, I study junctions between fractional quantum Hall (FQH) systems with different filling fractions. These junctions display a rich and interesting array of new physics. For example, I show that, by analyzing the scattering processes at the junction site, processes analogous to Andreev reflection present in superconductor/normal metal junctions are also present in the FQH junctions. I also analyze the noise spectrum of FQH junctions, and show that the scale of the noise spectrum is determined by the conductance of the junction. Furthermore, I discuss the implications of these results on the interpretation of recent experiments in terms of quasiparticles with fractional charge. Finally, I introduce the concept of generalized noise Wilson ratios as universal quotients between noise amplitudes in the thermal and shot noise regimes and discuss their experimental consequences.
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