Topological index for periodically driven time-reversal invariant 2D systems

Area of Science:

• Condensed Matter Physics
• Topological Matter
• Quantum Dynamics

Background:

• Periodically driven systems exhibit unique topological phases.
• Time-reversal symmetry is crucial for many topological invariants.
• Characterizing topological properties in driven systems remains challenging.

Purpose of the Study:

• To define a novel Z2-valued index for topological characterization.
• To relate this index to spectral gaps and existing topological invariants.
• To explore the implications for periodically driven 2D crystals.

Main Methods:

• Definition of a new Z2-valued topological index.
• Analysis of spectral gaps of the time-evolution operator.
• Derivation of the Kane-Mele invariant from the new index.
• Numerical modeling of a driven square lattice system.

Main Results:

• A new Z2-valued index is established for periodically driven 2D crystals.
• The index is directly linked to spectral gaps of the evolution operator.
• The Kane-Mele invariant is recovered and expressed via the Wess-Zumino amplitude.
• Numerical simulations confirm the index's relation to edge states.

Conclusions:

• The new index provides a robust tool for classifying topological phases in driven systems.
• This work establishes a connection between spectral properties and topological invariants.
• The findings offer a deeper understanding of topological phenomena in periodically driven matter.