Majorana mediated non-local charge dynamics in topological superconductors
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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.
Thesis, PhD Doctor of Philosophy