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

Understand

We define a new $Z_2$-valued index to characterize the topological properties of periodically driven two dimensional crystals when the time-reversal symmetry is enforced.

• This index is associated with a spectral gap of the evolution operator over one period of time.
• When two such gaps are present, the Kane-Mele index of the eigenstates with eigenvalues between the gaps is recovered as the difference of the gap indices.
• This leads to an expression for the Kane-Mele invariant in terms of the Wess-Zumino amplitude.