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Non-Abelian Quantum Hall States and Fractional Statistics


Bishara, Waheb (2009) Non-Abelian Quantum Hall States and Fractional Statistics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/WQC4-W268.


The discovery of the fractional quantum Hall effect stimulated the investigation of anyons, particles with fractional statistics which are neither bosons nor fermions. This thesis focuses on the study of quantum Hall states which may support non-Abelian anyons. We first address the validity of assumptions used in the numerical study of such states, and then proceed with analyzing different experiments which can detect non-Abelian fractional statistics. We quantitatively analyze the two-point contact interferometer experiment, which is hoped to display clear-cut, direct evidence of non-Abelian fractional statistics. We calculate the temperature and voltage dependence of the interference experiment outcome, and the signal attenuation due to finite temperature loss of coherence. We then analyze the edge theory of a family of non-Abelian quantum Hall states in the second Landau level, and examine the tunneling between these states and a quantum dot. This tunneling problem maps onto the multi-channel Kondo problem, and will allow distinguishing between different quantum Hall states. Finally, we use the same theoretical methods for analyzing Sagnac interference in the conductance of a carbon nanotube loop, a one-dimensional system.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Fractional Statistics; Non-Abelian Statistics; Quantum Hall; Topological Phases
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Nayak, Chetan
Thesis Committee:
  • Kitaev, Alexei (chair)
  • Nayak, Chetan (co-chair)
  • Refael, Gil
  • Motrunich, Olexei I.
Defense Date:5 May 2009
Record Number:CaltechETD:etd-05122009-142703
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1759
Deposited By: Imported from ETD-db
Deposited On:29 May 2009
Last Modified:26 Nov 2019 20:23

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