Rotating Zeeman field as a tool for Majorana zero mode detection in topological superconducting wire

We demonstrate that analysis of the spin polarization of a quantum dot (QD) attached to the topological wire can provide valuable insights into Majorana zero mode (MZM) formation and topological phase transition. Detection is realized by rotation of the Zeeman field in the wire, while retaining the Zeeman field direction in the dot intact. In the presence of Majorana mode, the effective QD spin polarization at Fermi energy changes significantly when the direction of the Zeeman field in the wire changes from parallel to perpendicular to the wire axis. It can be opposed to the wire in its trivial state, when spin polarization remains practically constant while the magnetic field is rotated. Similar unaltered spin polarization is observed when QD spin sub-level at Fermi energy mimics MZM. Moreover, the characteristic non-linear dependence of the spin polarization on the magnetic field magnitude at its critical value identifies a topological phase transition in the wire. This feature is observed independently on the coupling strength of the wire to the dot and the angle of the Zeeman field.