We explore the roles of topology and time-reversal symmetry in one-dimensional superconducting systems. Specifically, we examine junctions involving time-reversal-invariant topological superconductors, which are characterised by the emergence of zero-energy Majorana- Kramers pairs at their boundaries. For Josephson junctions composed of these superconductors, we obtain, through a scattering matrix technique valid in a regime where the junction length is much shorter than the superconducting coherence length, exact analytical and numerical results for the Josephson current in terms of a small number of independently measurable junction parameters. The current is found to have a number of prominent and robust features which indicate the underlying symmetries and the nontrivial topology inherent in these systems. The most remarkable of these features occurs in the form of switches in the Josephson current, where the sign of the current reverses as a consequence of crossings between energy levels in the subgap spectrum. By utilising a quantum master equation approach, we establish general conditions under which these switches manifest in relation to a phenomenological relaxation rate and a voltage applied across the junction. Our findings enable quantitative predictions for such junctions, potentially assisting in experimental directions regarding the detection of Majorana- Kramers pairs in mesoscopic Josephson systems.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:768290 |
| Date | January 2018 |
| Creators | Mellars, Ehren Axel |
| Publisher | University of Birmingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.bham.ac.uk//id/eprint/8739/ |
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