  The recent discoveries of higher-order topological insulators (HOTIs) have
shifted the paradigm of topological materials, which was previously limited to
topological states at boundaries of materials, to those at boundaries of
boundaries, such as corners . So far, all HOTI realisations have assumed static
equilibrium described by time-invariant Hamiltonians, without considering
time-variant or nonequilibrium properties. On the other hand, there is growing
interest in nonequilibrium systems in which time-periodic driving, known as
Floquet engineering, can induce unconventional phenomena including Floquet
topological phases and time crystals. Recent theories have attemped to combine
Floquet engineering and HOTIs, but there has thus far been no experimental
realisation. Here we report on the experimental demonstration of a
two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice,
with modulation along z axis serving as an effective time-dependent drive.
Direct acoustic measurements reveal Floquet corner states that have
time-periodic evolution, whose period can be even longer than the underlying
drive, a feature previously predicted for time crystals. The Floquet corner
states can exist alongside chiral edge states under topological protection,
unlike previous static HOTIs. These results demonstrate the unique space-time
dynamic features of Floquet higher-order topology.
