Dirac Semimetals with Hinge States

Dirac semimetals exhibit mid-gap boundary states localized at the intersections of surfaces, known as hinges, giving rise to higher-order Fermi arcs. These hinge states specifically will terminate at the projections of bulk Dirac points. To determine when Dirac points have hinge states that terminate on them, we derived the symmetry indicators, which predict the filling anomaly in two-dimensions. The change in the filling anomaly turns out to be a stable quantity that characterizes this problem. With the indicators, we classified Dirac semimetals and showed that all linear Dirac points at high symmetry lines have hinge states. Finally, we discuss the hinge states in the Dirac semimetal Na3Bi, in materials beyond Dirac semimetals, and in systems with commensurate magnetic field.