Weyl semimetallic state with antiferromagnetic order in the Rashba-Hubbard model

We study the phase diagram of the Rashba-Hubbard model by employing the Hartree-Fock mean-field theory and thereby establish the existence of an antiferromagnetically ordered Weyl semimetallic state with in-plane magnetic moments. This phase is found to be sandwiched between the antiferromagnetic insulator and Rashba metal in the interaction vs spin-orbit coupling phase diagram. The antiferromagnetically ordered topological semimetallic state exists in the presence of combined time-reversal and inversion symmetry, although individually both are broken. The study of the static magnetic susceptibility indicates the robustness of the antiferromagnetic order within a realistic range of interaction and spin-orbit coupling parameters. In addition to the edge states associated with the Weyl points, we also investigate the spin-resolved quasiparticle interference, which provides important insight into the possible spin texture of the bands, especially in the vicinity of Weyl points.