  The higher-order topological insulator (HOTI) is a new type of topological
system which has special bulkedge correspondence compared with conventional
topological insulators. In this work, we propose a scheme to realize Floquet
HOTI in ultracold atom systems. With the combination of periodically
spin-dependent driving of the superlattices and a next-next-nearest-neighbor
d-wave-like anisotropic coupling term between different spin components, a
Floquet second-order topological insulator with four zero-energy corner states
emerges, whose Wannier bands are gapless and exhibit interesting bulk topology.
Furthermore, the anisotropic coupling with nearest-neighbor form will also
induce some intriguing topological phenomena, e.g. non-topologically protected
corner states and topological semimetal for two different types of lattice
structures respectively. Our scheme may give insight into the construction of
different types of higher-order topological insulators in synthetic systems. It
also provides an experimentally feasible platform to research the relations
between different types of topological states and may have a wide range of
applications in future.
