Controlling And Manipulating The Topological Spin Of Majoranas

Majorana zero modes (MZMs) have attracted interest both for their fundamentalphysics and for their potential technological applications. While the non-Abelianphase associated with a braiding operation is widely recognized, the accompanyingAbelian phase of −π/4 does not enjoy the same level of recognition. The non-Abelianexchange statistics of Majorana zero modes make them suitable for potential applicationsin fault-tolerant quantum computation and topological quantum computingFor this reason, finding physical platforms capable of realizing these exotic quasiparticlesin condensed matter systems is an active area of research. In this thesis,we focus on the Abelian exchange phase of Majorana zero modes. We examinedthis phase in two well-known models of topological superconductors: the Fu-Kanemodel and hybrid structures of superconductor / quantum anomalous Hall (QAH)insulators. We demonstrated that this phase originates from an Aharonov-Casherphase generated by a superconducting vortex encircling a charge of −e/4 associatedwith the Fermi sea. Next, in two-dimensional (2D) systems, we showed thatthe fractional charge and the Majorana zero mode are co-located in the core of thesuperconducting vortex, whereas in three-dimensional (3D) systems, the fractionalcharge and the Majorana mode can be spatially separated. In doing so, we designeda heterostructure system that enables the manipulation of both the Abelian andnon-Abelian contributions of Majoranas. Finally, we proposed a superconductingvortex interference experiment capable of directly detecting the effects of the isolatedAbelian exchange phase discussed here.