Delocalisation of Majorana quasiparticles in plaquette--nanowire hybrid system

Abstract

Interplay between superconductivity, spin-orbit coupling and magnetic field can lead to realisation of the topologically non--trivial states which in finite one dimensional nanowires are manifested by emergence of a pair of zero-energy Majorana bound states. On the other hand, in two dimensional systems spin current contributed by the edge states might appear. We investigate novel properties of the bound states in a system of mixed dimensionality, composed of one-dimensional nanowire connected with two-dimensional plaquette. This setup could be patterned epitaxially, e.g. using heterostructure analogous to what has been reported recently by F. Nichele et al., Phys. Rev. Lett. 119, 136803 (2017). We study this system, assuming either its part or the entire structure to be in topologically non--trivial superconducting state. Our results predict delocalisation of the Majorana modes, upon leaking from the nanowire to the nanocluster with some tendency towards its corners.