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 C_(2).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 C_(2)=±3 to another topological phase with C_(2)=±1,or to a topological phase with an even second Chern number C_(2)=±2,which is absent in the 4D static system.Finally,the approximation theory in the high-frequency limit further confirms the numerical conclusions.