Floquet engineering with resonant drive and Application to symmetry-protected topological phases

Recently periodically driven (Floquet) systems have attracted much interested, and Floquet engineering, control of phases by a periodic drive, is one of the most vigorous fields in Floquet systems. However, in conventional Floquet engineering, only high-frequency drives (=drives whose energy scale is much smaller than the frequency) are mainly utilized since it is based on high-frequency expansion theory, only applicable to Floquet systems under high-frequency drives.
Therefore, we extend the conventional high-frequency expansion theory to the cases in the presence of resonant drives (= drives whose local energy scale is comparable to the frequency) and propose a new scheme of Floquet engineering done by high-frequency and resonant drives [1]. We clarify that the effective Hamiltonian describing long-time dynamics acquires an emergent Z_N symmetry, and hence our scheme enables us to simultaneously control phases and add a symmetry to the system. With our Floquet engineering, we also propose a way to realize/control topological phases protected by a Z_2×Z_2 symmetry only in the presence of a Z_2 symmetry [2].

[References]
[1] K. Mizuta, et al., PRB 100, 020301(R) (2019)
[2] K. Mizuta, et al., arXiv: 1908.04100 (2019)