  This work reports the general design and characterization of two exotic,
anomalous nonequilibrium topological phases. In equilibrium systems, the Weyl
nodes or the crossing points of nodal lines may become the transition points
between higher-order and first-order topological phases defined on
two-dimensional slices, thus featuring both hinge Fermi arc and surface Fermi
arc. We advance this concept by presenting a strategy to obtain, using
time-sequenced normal insulator phases only, Floquet higher-order Weyl
semimetals and Floquet higher-order nexus semimetals, where the concerned
topological singularities in the three-dimensional Brillouin zone border
anomalous two-dimensional higher-order Floquet phases. The fascinating
topological phases we obtain are previously unknown and can be experimentally
studied using, for example, a three-dimensional lattice of coupled ring
resonators.
