Nodal lines and boundary modes in topological dirac semimetals with magnetism

While nodal-line semimetals with magnetism have been theoretically predicted and experimentally observed in a few compounds, idea on the relation between the magnetic order and the electronic structure is still limited. We theoretically explore the electronic structure in bulk and boundary of such a magnetic nodal-line state by introducing magnetism in topological Dirac semimetal (TDSM). TDSMs, such as Cd₃As₂ and Na₃Bi, are characterized by a pair of spin-degenerate Dirac points protected by rotational symmetries of crystals. By introducing local magnetic moments coupled to the electron spins in the lattice model of TDSM, we show that the TDSM can turn into either a Weyl semimetal or a nodal-line semimetal, which is determined by the orbital dependence in the exchange coupling and the direction of magnetization formed by the magnetic moments. In this magnetic nodal-line semimetal state, we find zero modes with drumhead-like band structure at the boundary that are characterized by the topological number of Z. Those zero modes are numerically demonstrated by introducing magnetic domain walls in the lattice model.