PhD Thesis: Non-local behaviour from local interactions
Tuesday 10 October 2017
to 16:00 at
The Oskar Klein auditorium (lecture hall FR4)
Thomas Kvorning (Stockholm University, Department of Physics)
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
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
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.