  The hybrid nanowire consisting of semiconductor with proximity to
superconductor is expected to serve as an experimental platform to display
Majorana zero modes. By rederiving its effective Kitaev model with spins, we
discover a novel topological phase diagram, which assigns a more precise
constraint on the magnetic field strength for the emergence of Majorana zero
modes. It then turns out 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 as 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
$2e^{2}/h$ in the differential conductance spectrum, as the necessary evidence
for the Majorana zero modes, disappears when the magnetic field grows too
strong. For illustrations with practical hybrid systems, in the InSb nanowire
coupled to NbTiN, the accessible magnetic field range is around 0.1--1.5T; when
coupled to aluminum shell, the accessible magnetic field range should be
smaller than 0.12T. These predictions obviously clarify the current
controversial issues about some experiments of Majorana zero modes with hybrid
nonawire.
