Tuning Second Chern Number in a Four-Dimensional Topological Insulator by High-Frequency Time-Periodic Driving

Floquet engineering has attracted considerable attention as a promising approach for tuning topological phase transitions. We investigate the effects of high-frequency time-periodic driving in a four-dimensional (4D) topological insulator, focusing on topological phase transitions at the off-resonant quasienergy gap. The 4D topological insulator hosts gapless three-dimensional boundary states, characterized by the second Chern number C₂. We demonstrate that the second Chern number of 4D topological insulators can be modulated by tuning the amplitude of time-periodic driving. This includes transitions from a topological phase with C₂ = ±3 to another topological phase with C₂ = ±1, or to a topological phase with an even second Chern number C₂ = ±2, which is absent in the 4D static system. Finally, the approximation theory in the high-frequency limit further confirms the numerical conclusions.