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 \(\mathbb{Z}\). Those zero modes are numerically demonstrated by introducing magnetic domain walls in the lattice model.

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具有磁性的拓扑狄拉克半金属中的节点线和边界模式

虽然在一些化合物中已经从理论上预测和实验观察到具有磁性的节点线半金属，但关于磁性顺序与电子结构之间关系的想法仍然有限。我们通过在拓扑狄拉克半金属（TDSM）中引入磁性，从理论上探索了这种磁节点线态的体电子结构和边界。TDSM，例如 Cd ₃ As ₂和 Na ₃Bi 的特点是一对自旋简并狄拉克点受到晶体旋转对称性的保护。通过在 TDSM 的晶格模型中引入耦合到电子自旋的局部磁矩，我们表明 TDSM 可以变成 Weyl 半金属或节点线半金属，这是由交换耦合中的轨道依赖性和方向决定的由磁矩形成的磁化强度。在这种磁节点线半金属态中，我们在边界处找到了具有鼓面状能带结构的零模式，其特征在于拓扑数\(\mathbb{Z}\). 这些零模式通过在晶格模型中引入磁畴壁来进行数值演示。