Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s – d -hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- ( α ) and intermediate-temperature ( α ″ ) phases of Cd 3 As 2 , KMgBi, and rutile-structure ( β ′ -) PtO 2 . The existence of a topological bulk-boundary correspondence for Dirac semimetals has remained an open question. Here, Wieder et al. predict one-dimensional hinge states originating from bulk three-dimensional Dirac points in solid-state Dirac semimetals, revealing condensed matter Dirac fermions to be higher-order topological.