Intermediate gapless phase and topological phase transition of the Kitaev model in a uniform magnetic field

We study the Kitaev model in a [001] magnetic field employing the mean-field theory(MFT) in the Majorana fermion representation. We discover a robust gapless regime in the intermediate magnetic field for both gapless and gapped antiferromagnetic(AFM) Kitaev models with Jx = Jy before the system is polarized in a high magnetic field. A topological phase transition connecting two gapless phases with a nodal line phase takes place at a critical magnetic field h_c1 in this regime. While the nodal line phase at h_c1 disappears when the mirror symmetry Jx = Jy is broken, the nodal point gapless phase can exist at intermediate fields even without the mirror symmetry. We reveal that the phase evolution of the system in the magnetic field is driven by the competition between the magnetic field and the particle-hole asymmetry of the normal state of the BdG Hamiltonian. For the ferromagnetic case, there is no intermediate phase transition before polarization. The above phase diagrams are confirmed by dynamical MFT results.