Influence of the orbital effects on the Majorana quasi-particles in a nanowire

Majorana quasi-particles can be realised using magnetic field in the form of diamagnetic (orbital) or paramagnetic effects. In both cases, the magnetic field induces a topologically non-trivial phase of matter. In this paper, the influence of orbital effects on Majorana bound states induced by paramagnetic effects in 1D nanowire is elaborated. The role of orbital effects in density of states and eigenstates of the system is also discussed. Additionally, we show the phase diagram-the magnetic field versus the magnetic flux, which displays a relation between topologically trivial and non-trivial phases. The Majorana bound states existence in the presence of relatively small orbital effects is indicated.