Second-order topological insulator in periodically driven optical lattices.

Area of Science:

• Condensed Matter Physics
• Quantum Simulation
• Topological Matter

Background:

• Higher-order topological insulators (HOTIs) represent a novel class of topological materials with unique bulk-edge correspondence.
• Conventional topological insulators exhibit protected edge states, while HOTIs feature topological states at lower-dimensional boundaries (e.g., corners).

Purpose of the Study:

• To propose and theoretically investigate a scheme for realizing a Floquet higher-order topological insulator using ultracold atoms in optical lattices.
• To explore the emergence of topological phenomena, such as corner states, in synthetic quantum systems.

Main Methods:

• Utilizing ultracold atoms in optical lattices subjected to periodically driven superlattices with spin-dependent forces.
• Incorporating a long-range coupling term and nearest-neighbor anisotropic coupling to engineer the desired topological phases.
• Analyzing the bulk topology and band structures, including gapless Wannier bands.

Main Results:

• Demonstrated the emergence of a Floquet second-order topological insulator with four zero-energy corner states.
• Observed gapless Wannier bands with interesting bulk topology.
• Identified other topological phenomena, including non-topologically protected corner states and topological semimetals, in different lattice structures.

Conclusions:

• The proposed scheme provides a feasible platform for realizing and studying Floquet higher-order topological insulators in synthetic systems.
• This work offers insights into the construction of various HOTI types and the relationships between different topological states.
• The findings may pave the way for future applications in topological quantum technologies.