  Placed in cavity resonators with three-dimensionally confined electromagnetic
wave, the interaction between quasiparticles in solids can be induced by
exchanging virtual cavity photons, which can have a non-local characteristic.
Here we investigate the possibility of utilizing this nonlocality to realize
the remote control of the topological transition in mesoscopic moir\'{e}
superlattices at full filling (one electron/hole per supercell) embedded in a
split-ring terahertz electromagnetic resonator. We show that gate tuning one
moir\'{e} superlattice can remotely drive a topological band inversion in
another moir\'{e} superlattice not in contact but embedded in the same cavity.
Our study of remote on/off switching of a topological transition provides a
novel paradigm for the control of material properties via cavity vacuum fields.

Materials Science;Mesoscale and Nanoscale Physics