Majorana bound states in nanowire junctions

Abstract

\n The possible realization of Majorana quasiparticles in condensed matter systems has motivated much research over the last decade, as it might pave the ground for topological quantum computing devices. In this work we review important concepts and results in the area, such as non-Abelian anyons, the Kitaev model and braiding. We then turn to a proposed implementation of Majorana fermions by reproducing literature results showing the emergence of p-wave superconductivity in nanowires with Rashba spin-orbit coupling and s-wave superconductivity in external magnetic fields. We study the spectrum for both infinite and finite nanowires and its evolution with respect to the field strength. We show that a topological phase transition is achieved and the emergence of Majorana Bound States (MBSs) in the topological phase. We investigate the distribution of these states across the nanowire and their non-locality. We then reproduce results of NS and SNS junctions with Rashba nanowires, showing the leaking of the edge states into the normal regions. We also study the effects of the superconducting phase difference across the SNS junction, in particular how MBSs emerge at the interfaces only for a phase difference of pi. We then calculate the Josephson current across the junction for different regimes and find a signature for the presence of MBSs. Finally, we propose a quantitative measurement for this signature through the derivative of the supercurrent for a phase difference of pi.\n