Licentiate Thesis: Topology in One-Dimensional Quantum Systems
Tuesday 09 June 2015
to 12:00 at
Christian Spånslätt (Stockholm University, Department of Physics)
States of matter which are described by concepts in topology are of great interest in the
community of condensed matter physics. Both from a pure theoretical perspective, where
many non-intuitive and mathematically rich results can be found from seemingly simple
models, and also since recent experimental developments allows for explicit construction of
devices where the underlying topology has observable consequences.
This thesis provides a conceptual introduction to the framework describing such topological
states of matter (TSM). It starts by explaining ordinary band theory which is followed by a
discussion of quantum mechanical symmetries. These two concepts provides a method of
classifying all non-interacting fermionic TSM. Following are explicit applications to a few
models in one spatial dimension.
In the accompanying paper, we study one-dimensional superconductors with Josephsonjunctions
allowing phase shifts of π. We make a detailed analysis of the junction bound states
and their properties in some different settings and compare the behaviour of trivial and
topological superconducting junctions. In addition, we provide a phenomenological
topological field theory in the low energy limit.