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Quantum Hall ferromagnets and transport properties of buckled Dirac materials

We study the ground states and low-energy excitations of a generic Dirac material with spin-orbit coupling and a buckling structure in the presence of a perpendicular magnetic field. The ground states can be classified into three types under different conditions: SU(2), easy-plane, and Ising quantum Hall ferromagnets. For the SU(2) and the easy-plane quantum Hall ferromagnets there are goldstone modes in the collective excitations, while all the modes are gapped in an Ising-type ground state. We compare the Ising quantum Hall ferromagnet with that of bilayer graphene and present the domain wall solution at finite temperatures. We then specify the phase transitions and transport gaps in silicene in Landau levels 0 and 1. The phase diagram strongly depends on the magnetic field and the dielectric constant. We note that there exists triple points in the phase diagrams in Landau level N = 1 that could be observed in experiments.