Effect of magnetic field orientation and disorder on Majorana polarization in wires with topological superconductivity

Abstract

Majorana polarization, previously introduced by Sticlet et al. [Phys. Rev. Lett. 108, 096802 (2012)], is studied for wires in a topological superconductive state with varying orientation of the magnetic field. Numerical calculations show that in the case of a canted field, this polarization can differ in sign, as well as absolute magnitude, at the opposite ends of a wire. Since the Majorana polarization changes sign at one end when the orientation of the magnetic field is changed from perpendicular to longitudinal, there is always a range of angles for which this quantity is significantly suppressed or equals zero. Thus, the Majorana polarization does not always appear as a local order parameter for an arbitrary angle of the magnetic field in the plane perpendicular to the effective Rashba spin-orbital interaction field. It is shown that the introduction of disorder does not lead to qualitatively new effects. At the same time, additional regions with weak Majorana polarization do show up in high magnetic ...