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Quantum Hall hierarchy in a spherical geometry
Stockholm University, Faculty of Science, Department of Physics.
2013 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 87, no 19, 195131Article in journal (Refereed) Published
Abstract [en]

Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until now, the constructions have been restricted to flat geometries, but in this paper we generalize to the simplest curved geometry, namely that of a sphere. Except for being of interest for numerical studies, that usually are performed on a sphere, the response of the fractional quantum Hall (FQH) liquids to curvature can be used to detect a topological quantity, the shift S which is the average orbital spin of the constituent electrons. We give explicit expressions for representative wave functions on the sphere, for the full Abelian FQH hierarchy, and calculate the corresponding shifts. These microscopic results, based on wave functions, agree with the predictions from the effective Chern-Simons field theory. The methods we develop can also be applied to the planar case. It gives simpler expressions for states with both quasiparticle and quasihole condensates, and allows us to give closed form expressions for a general state in the hierarchy, rather than finding the wave function on a case by case basis.

Place, publisher, year, edition, pages
2013. Vol. 87, no 19, 195131
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-91837DOI: 10.1103/PhysRevB.87.195131ISI: 000319391000001OAI: oai:DiVA.org:su-91837DiVA: diva2:636027
Note

AuthorCount:1;

Available from: 2013-07-08 Created: 2013-07-04 Last updated: 2017-08-29Bibliographically approved
In thesis
1. Non-local behaviour from local interactions
Open this publication in new window or tab >>Non-local behaviour from local interactions
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

With the discovery of the quantum Hall effect more than thirty years ago, a whole new field emerged—that of topological quantum matter. This field is now a very mature one, and many different aspects are covered in the literature. The main text of this thesis introduces the field and gives a background to topological quantum matter, as well as topological aspects of superconductivity and the Abelian fractional quantum Hall (FQH) states.

 Together with the main text there are five articles that address five different questions, all connected to topological quantum matter.

In the first article, representative wave functions for the Abelian FQH states are calculated using conformal field theory methods. Before this paper was published, similar constructions had been restricted to flat geometries, but in this paper we generalize the analysis to the simplest curved geometry, namely the sphere. On top of being of interest for numerical studies (which usually are performed on a sphere), the response of the FQH liquids to curvature can be used to detect a topological quantity, the shift, which is the average orbital spin of the constituent electrons.

In the second article, we construct an effective field theory for the two-dimensional spinless, chiral p-wave superconductor that faithfully describes the topological properties of the bulk state, and also provides a model for the subgap states at vortex cores and edges. In particular, it captures the topologically protected zero-modes and has the correct ground state degeneracy on the torus.

In the third paper, tools for a hydrodynamic theory for insulators in three dimensions are derived. Specifically, we use functional bosonization to write insulators as a condensation phase of the U(1) gauge theory obtained in the functional bosonization language.

In the fourth paper, we investigate the edge Majorana modes in the two-dimensional chiral p-wave superconductor. We define the model on surfaces with different geometries—the annulus, the cylinder, the Möbius band, and a cone—and with different configurations of magnetic flux threading holes in these surfaces. In particular, we address the following question: Given that, in the absence of magnetic flux, the ground state on the annulus does not support Majorana modes, while the one on the cylinder does, how is it possible that the conical geometry can interpolate smoothly between the two?

In the fifth and last article, we demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. We propose this geo-Meissner effect as an unequivocal signature of chiral superconductivity that could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of Majorana modes.

 

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2017. 95 p.
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-146296 (URN)978-91-7649-954-2 (ISBN)978-91-7649-955-9 (ISBN)
Public defence
2017-10-10, The Oskar Klein auditorium (lecture hall FR4), AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 5: Manuscript.

Available from: 2017-09-15 Created: 2017-08-29 Last updated: 2017-09-06Bibliographically approved

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