Floquet Second-Order Topological Insulators from Nonsymmorphic Space-Time Symmetries

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Quantum Physics

Background:

• Topological insulators (TIs) exhibit unique electronic properties protected by symmetry.
• Second-order topological insulators (SOTIs) host protected boundary states at lower dimensions.
• Floquet systems, driven by time-periodic potentials, offer new avenues for topological phases.

Purpose of the Study:

• To develop a systematic method for constructing Floquet second-order topological insulators (SOTIs).
• To leverage time-glide symmetry for creating novel Floquet topological phases.
• To provide a practical framework for experimental realization of Floquet SOTIs.

Main Methods:

• Introducing time-glide symmetry, a novel nonsymmorphic space-time symmetry in Floquet systems.
• Analyzing the enlarged static Hamiltonian in the frequency domain to reveal emergent reflection symmetry.
• Utilizing established methods for static SOTIs to construct their Floquet counterparts.

Main Results:

• Demonstrated that time-glide symmetry in Floquet systems leads to reflection symmetry in the enlarged static Hamiltonian.
• Showcased the construction of various time-glide symmetric Floquet SOTIs by adapting static SOTI designs.
• Confirmed that approximate implementation of time-glide symmetry is sufficient for practical realization.

Conclusions:

• Time-glide symmetry provides a powerful and systematic route to engineer Floquet SOTIs.
• The proposed method offers a versatile recipe applicable across different symmetry classes.
• This work significantly enhances the prospects for experimental observation and application of Floquet topological materials.