Universal role of combined symmetry for the protection of the Dirac cone in antiferromagnetic topological insulators

Antiferromagnetic topological insulators (AFM TIs) are predicted to exhibit exotic physical properties such as gigantic optical and topological magnetoelectric responses. While a key to achieving such phenomena relies on how to break the symmetry protecting the Dirac-cone surface state (SS) and acquire the mass of Dirac fermions, the mechanism has yet to be clarified. To address this issue, we carried out microfocused angle-resolved photoemission spectroscopy for GdBi hosting the type-II AFM order, and uncovered the stripe-type $2\times 1$ reconstruction of the Fermi surface associated with the AFM band folding. Intriguingly, in contrast to NdBi with the type-I AFM order displaying the surface-selective Dirac-fermion mass, GdBi shows massless behavior irrespective of AFM domains due to the robust topological protection. These results strongly suggest a crucial role of the $\Theta T_D$ (time-reversal and translational) symmetry to create the Dirac-fermion mass in AFM TIs.