Topology has enjoyed great success as a paradigm for the classification and understandingof condensed matter outside the framework of spontaneously brokensymmetry. This success is all the more remarkable considering that the impact ofinteractions, in particular the Coulomb interaction between electrons, has been neglectedin most analyses. Experience in topologically trivial systems demonstratesthat, beyond simply leading to quantitative modifications, interactions can give riseto qualitatively new physics in condensed matter. This thesis explores the interplaybetween interaction effects and topologically non-trivial states and demonstrateshow this interplay can lead to novel physics which is fundamentally contingent uponboth a system's topological character and interactions.The prototypical example of a topological state in condensed matter is the Majoranabound state (MBS). In the work presented here, MBSs are significant because theylead to non-local fermionic states in superconductors that are bound to near-zeroenergy, inside the superconducting gap. The new physics arising from the synergyof MBSs and electron-electron interactions is illustrated by two examples. AMajorana-based analogue of the Kondo system is found to exhibit signs of a delocalisedmany-body state consisting of electrons from both metallic leads and asuperconducting condensate. The presence of MBSs in a current driven capacitiveJosephson junction enables excitation of the system to a non-equilibrium state andprofoundly affects the overall charge dynamics of the junction.This thesis offers compelling evidence for the importance of interactions in the contextof topologically non-trivial systems, not only with regard to determining thetopology of the system per se, but also as the means by which new physics is realised.
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Majorana mediated non-local charge dynamics in topological superconductors
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