Majorana fermions in finite-size strips in the presence of orbital effects: what is the Majorana polarization telling us?

We study numerically the formation of Majorana bound states in a finite-size quasi-one-dimensional square-lattice strip with Rashba spin-orbit coupling, in the presence of a proximity-induced superconducting pairing and a magnetic field perpendicular to the strip. We take into account both the Zeeman and orbital effects of the field. First, using the Majorana polarization, we demonstrate that such a system can host more than one pair of Majorana quasiparticles. We construct the corresponding topological phase diagram and we conclude that the topological regions are extended in the presence of orbital effects, however the gap protecting the topological states is reduced.