Majorana bound states in inhomogeneous nanowires

Abstract: Majorana bound states are in condensed matter physics quasiparticle excitations which can be found in so-called topological superconductors. They have lately received much attention since they have been predicted to be partly immune to decoherence and therefore suitable for quantum computation. A nanowire with strong spin orbit coupling and proximity induced superconductivity that is subject to a magnetic field has been shown to host a pair of Majorana bound states living on the opposite ends of the nanowire. One bit of quantum information (a qubit) can be stored in such a pair of Majorana bound states. The quantum information is then protected from decoherence as long as the Majorana bound states are well separated, such that their wave functions do not overlap. In this work we explore the effect of introducing potential barriers in the nanowire. It is shown that for certain parameter settings of the barriers the overlap between the Majorana bound states can be reduced. Furthermore, disorder in the potential is studied. The effect of the disorder is also shown to depend on the parameter settings of the barriers. Finally it is shown that a rotating magnetic field can amplify the spin-orbit coupling in a nanowire. Increasing the spin-orbit coupling results in a decrease in the overlap.