Dirac semimetals lack a simple bulk-boundary correspondence. Recently, Dirac materials with fourfold rotation symmetry have been shown to exhibit a higher-order bulk-hinge correspondence: they display “higher-order Fermi arcs,” which are localized on hinges where two surfaces meet and connect the projections of the bulk Dirac points. In this paper, we classify higher-order Fermi arcs for Dirac semimetals protected by a rotation symmetry and the product of time-reversal and inversion. Such Dirac points can be either linear in all directions or linear along the rotation axis and quadratic in other directions. By computing the filling anomaly for momentum-space planes on either side of the Dirac point, we find that all linear Dirac points exhibit higher-order Fermi arcs terminating at the projection of the Dirac point, while the Dirac points that are quadratic in two directions lack such higher-order Fermi arcs. When higher-order Fermi arcs do exist, they obey either a ${\mathbb{Z}}_2$ (fourfold rotation axis) or ${\mathbb{Z}}_3$ (three- or sixfold rotation axis) group structure. Finally, we build two models with sixfold symmetry to illustrate the cases with and without higher-order Fermi arcs. We predict higher-order Fermi arcs in ${\mathrm{Na}}_3\mathrm{Bi}$.

中文翻译：

---

具有高阶费米弧的狄拉克点的分类

狄拉克半金属缺乏简单的体边界对应关系。最近，具有四重旋转对称性的狄拉克材料已被证明表现出高阶体铰链对应：它们显示出“高阶费米弧”，其位于铰链上，其中两个表面相交并连接体体狄拉克点的投影. 在本文中，我们对受旋转对称性保护的狄拉克半金属的高阶费米弧以及时间反转和反演的产物进行分类。这样的狄拉克点可以在所有方向上都是线性的，也可以沿着旋转轴呈线性，在其他方向上是二次的。通过计算狄拉克点两侧动量空间平面的填充异常，我们发现所有线性狄拉克点都表现出终止于狄拉克点投影的高阶费米弧，而在两个方向上都是二次的狄拉克点缺乏这种高阶费米弧。当高阶费米弧确实存在时，它们服从${\mathbb{Z}}_2$ （四重旋转轴）或 ${\mathbb{Z}}_3$（三或六倍旋转轴）组结构。最后，我们建立了两个具有六重对称性的模型来说明有和没有高阶费米弧的情况。我们预测高阶费米弧${钠}_3双$.