  We generalize the nested Wilson loop formalism, which has been playing an
important role in the study of topological quadrupole insulators, to
two-dimensional (2D) and 3D nonsymmorphic materials with higher-order topology.
In particular, certain 3D Dirac semimetals exhibit 1D higher-order Fermi arc
(HOFA) states localizing on hinges where two surfaces meet and connecting the
projection of the bulk Dirac points. We discover that the generalized nested
Berry phase (gNBP) derived from this formalism is the bulk topological
indicator determining the existence/absence of HOFAs, revealing a direct
bulk-hinge correspondence in 3D Dirac semimetals. Finally, we study the Dirac
semimetals NaCuSe and KMgBi based on first-principles calculations and
explicitly show that the change in gNBP adjacent to the Dirac point corresponds
to the termination of HOFAs at the projection of Dirac points on the hinge. Our
findings not only improve the understanding of the bulk-hinge correspondence in
topological Dirac semimetals but also provide a general formalism for studying
the higher-order topology in nonsymmorphic systems.
