Magnetic field constraint for Majorana zero modes in a hybrid nanowire

The hybrid semiconductor-superconductor nanowire is expected to serve as an experimental platform to support Majorana zero modes. By rederiving its effective Kitaev model with spins, we discover a topological phase diagram, which assigns a more precise constraint on the magnetic field strength for the emergence of Majorana zero modes. We find that the effective pairing strength dressed by the proximity effect exhibits a significant dependence on the magnetic field, and thus the topological phase region is refined into a closed triangle in the phase diagram with chemical potential vs Zeeman energy (which is obviously different from the open hyperbolic region known before). This prediction is confirmed again by an exact calculation of quantum transport, where the zero bias peak of 2e2/h in the differential conductance spectrum, as the necessary evidence for the Majorana zero modes, disappears when the magnetic field grows too strong. Therefore, the hybrid nanowire system does not support Majorana zero modes under a too strong magnetic field. For illustrations with practical hybrid systems, in the InSb nanowire coupled to NbTiN, the accessible magnetic field range is around 0.1-1.5 T; when coupled to an aluminum shell, the accessible magnetic field range should be smaller than 0.12 T. Our predictions are essential to significantly narrow down the range of magnetic fields for further searching Majorana zero modes in experiments.