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The hybrid nanowire consisting of semiconductor with proximity tosuperconductor is expected to serve as an experimental platform to displayMajorana zero modes. By rederiving its effective Kitaev model with spins, wediscover a novel topological phase diagram, which assigns a more preciseconstraint on the magnetic field strength for the emergence of Majorana zeromodes. It then turns out the effective pairing strength dressed by theproximity effect exhibits a significant dependence on the magnetic field, andthus the topological phase region is refined as a closed triangle in the phasediagram with chemical potential vs. Zeeman energy(which is obviously differentfrom the open hyperbolic region known before). This prediction is confirmedagain by an exact calculation of quantum transport, where the zero bias peak of$2e^{2}/h$ in the differential conductance spectrum, as the necessary evidencefor the Majorana zero modes, disappears when the magnetic field grows toostrong. For illustrations with practical hybrid systems, in the InSb nanowirecoupled to NbTiN, the accessible magnetic field range is around 0.1--1.5T; whencoupled to aluminum shell, the accessible magnetic field range should besmaller than 0.12T. These predictions obviously clarify the currentcontroversial issues about some experiments of Majorana zero modes with hybridnonawire.

Do Majorana zero modes emerge in the hybrid nanowire under a strong magnetic field?