Time-periodic corner states from Floquet higher-order topology

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Acoustics

Background:

• Higher-order topological insulators (HOTIs) expand topological states to boundaries of boundaries, like corners.
• Existing HOTI realizations are limited to static systems, excluding time-dependent phenomena.
• Floquet systems, driven periodically in time, exhibit unique topological phases and time crystals.

Purpose of the Study:

• To experimentally realize a two-dimensional (2D) Floquet higher-order topological insulator (HOTI).
• To investigate the properties of topological states in a driven system.
• To explore the interplay between Floquet engineering and higher-order topology.

Main Methods:

• Fabrication of a three-dimensional (3D) acoustic lattice.
• Implementation of spatial modulation to emulate effective time-dependent driving (Floquet engineering).
• Acoustic measurements to detect and characterize topological states.

Main Results:

• Experimental demonstration of a 2D Floquet HOTI in the 3D acoustic lattice.
• Observation of topological corner states with oscillations at double the drive period.
• Demonstrated topological protection of these corner states, analogous to time crystal robustness.

Conclusions:

• Space-time dynamics can induce anomalous higher-order topological phases unique to Floquet systems.
• This work bridges the gap between Floquet engineering and higher-order topology experimentally.
• The findings pave the way for exploring novel topological phenomena in driven quantum and classical systems.