Topology has enjoyed great success as a paradigm for the classification and understanding
of condensed matter outside the framework of spontaneously broken
symmetry. This success is all the more remarkable considering that the impact of
interactions, in particular the Coulomb interaction between electrons, has been neglected
in most analyses. Experience in topologically trivial systems demonstrates
that, beyond simply leading to quantitative modifications, interactions can give rise
to qualitatively new physics in condensed matter. This thesis explores the interplay
between interaction effects and topologically non-trivial states and demonstrates
how this interplay can lead to novel physics which is fundamentally contingent upon
both a system's topological character and interactions.
The prototypical example of a topological state in condensed matter is the Majorana
bound state (MBS). In the work presented here, MBSs are significant because they
lead to non-local fermionic states in superconductors that are bound to near-zero
energy, inside the superconducting gap. The new physics arising from the synergy
of MBSs and electron-electron interactions is illustrated by two examples. A
Majorana-based analogue of the Kondo system is found to exhibit signs of a delocalised
many-body state consisting of electrons from both metallic leads and a
superconducting condensate. The presence of MBSs in a current driven capacitive
Josephson junction enables excitation of the system to a non-equilibrium state and
profoundly affects the overall charge dynamics of the junction.
This thesis offers compelling evidence for the importance of interactions in the context
of topologically non-trivial systems, not only with regard to determining the
topology of the system per se, but also as the means by which new physics is realised.Funded via " EPSRC Grant No. EP/I007002/1." -- Acknowledgement
