Title: Landau-Zener transitions for Majorana fermions,
Abstract: One-dimensional systems obtained as low-energy limits of hybrid
superconductor-topological insulator devices provide means of production,
transport, and destruction of Majorana bound states (MBSs) by variations of the
magnetic flux. When two or more pairs of MBSs are present in the intermediate
state, there is a possibility of a Landau-Zener transition, wherein even a slow
variation of the flux leads to production of a quasiparticle pair. We study
numerically a version of this process, with four MBSs produced and subsequently
destroyed, and find that, quite universally, the probability of quasiparticle
production in it is 50%. This implies that the effect may be a limiting factor
in applications requiring a high degree of quantum coherence.