  Three-dimensional higher-order topological semimetals in crystalline systems
exhibit higher-order Fermi arcs on one-dimensional hinges, challenging the
conventional bulk-boundary correspondence. However, the existence of
higher-order Fermi arc states in aperiodic quasicrystalline systems remains
uncertain. In this work, we present the emergence of three-dimensional
quasicrystalline second-order topological semimetal phases by vertically
stacking two-dimensional quasicrystalline second-order topological insulators.
These quasicrystalline topological semimetal phases are protected by rotational
symmetries forbidden in crystals, and are characterized by topological hinge
Fermi arcs connecting fourfold degenerate Dirac-like points in the spectrum.
Our findings reveal an intriguing class of higher-order topological phases in
quasicrystalline systems, shedding light on their unique properties.
