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Quasiparticles in the Quantum Hall Effect
Stockholm University, Faculty of Science, Department of Physics.
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The fractional quantum Hall effect (FQHE), discovered in 1982 in a two-dimensional electron system, has generated a wealth of successful theory and new concepts in condensed matter physics, but is still not fully understood. The possibility of having nonabelian quasiparticle statistics has recently attracted attention on purely theoretical grounds but also because of its potential applications in topologically protected quantum computing.

This thesis focuses on the quasiparticles using three different approaches. The first is an effective Chern-Simons theory description, where the noncommutativity imposed on the classical space variables captures the incompressibility. We propose a construction of the quasielectron and illustrate how many-body quantum effects are emulated by a classical noncommutative theory.

The second approach involves a study of quantum Hall states on a torus where one of the periods is taken to be almost zero. Characteristic quantum Hall properties survive in this limit in which they become very simple to understand. We illustrate this by giving a simple counting argument for degeneracy 2n-1, pertinent to nonabelian statistics, in the presence of 2n quasiholes in the Moore-Read state and generalise this result to 2n-k quasiholes and k quasielectrons.

In the third approach, we study the topological nature of the degeneracy 2n-1 by using a recently proposed analogy between the Moore-Read state and the two-dimensional spin-polarized p-wave BCS state. We study a version of this problem where one can use techniques developed in the context of high-Tc superconductors to turn the vortex background into an effective gauge field in a Dirac equation. Topological arguments in the form of index theory gives the degeneracy 2n-1 for 2n vortices.

Place, publisher, year, edition, pages
Stockholm: Fysikum , 2006. , 102 p.
Keyword [en]
quantum Hall effect, quasiparticles, noncommutative Chern-Simons theory, nonabelian statistics, thin torus, p-wave superconductivity, topology, index theory, effective gauge fields
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:su:diva-1250ISBN: 91-7155-320-7 (print)OAI: oai:DiVA.org:su-1250DiVA: diva2:189701
Public defence
2006-09-27, sal FD5, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 09:30
Opponent
Supervisors
Available from: 2006-09-01 Created: 2006-09-01 Last updated: 2013-04-29Bibliographically approved
List of papers
1. Charge and current in the quantum Hall matrix model
Open this publication in new window or tab >>Charge and current in the quantum Hall matrix model
2003 In: Physical Review B, Vol. 68, 035327- p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-22896 (URN)
Note
Part of urn:nbn:se:su:diva-1250Available from: 2006-09-01 Created: 2006-09-01Bibliographically approved
2. Solitons and quasielectrons in the quantum Hall matrix model
Open this publication in new window or tab >>Solitons and quasielectrons in the quantum Hall matrix model
2005 In: Physical Review B, Vol. 72, 205317- p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-22897 (URN)
Note
Part of urn:nbn:se:su:diva-1250Available from: 2006-09-01 Created: 2006-09-01Bibliographically approved
3. Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus
Open this publication in new window or tab >>Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus
Show others...
2006 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 74, no 8, 081308- p.Article in journal (Refereed) Published
Abstract [en]

We analyze the Moore-Read Pfaffian state on a thin torus. The known sixfold degeneracy is realized by two inequivalent crystalline states with a four- and twofold degeneracy, respectively. The fundamental quasihole and quasiparticle excitations are domain walls between these vacua, and simple counting arguments give a Hilbert space of dimension 2n−1 for 2n−k holes and k particles at fixed positions and assign each a charge ±e∕4. This generalizes the known properties of the hole excitations in the Pfaffian state as deduced using conformal field theory techniques. Numerical calculations using a model Hamiltonian and a small number of particles support the presence of a stable phase with degenerate vacua and quarter-charged domain walls also away from the thin-torus limit. A spin-chain Hamiltonian encodes the degenerate vacua and the various domain walls.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-24938 (URN)10.1103/PhysRevB.74.081308 (DOI)000240238900011 ()
Available from: 2008-05-01 Created: 2008-05-01 Last updated: 2017-12-13Bibliographically approved

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