Cavity vacuum control of topological transition in a full filling moiré superlattice

The interaction between quasiparticles in condensed matter systems induced by exchanging virtual photons has attracted widespread interest because it leads to remarkable and exotic phases of matter. Such virtual-photon-mediated interaction is typically investigated in a strong light-matter coupling regime realized in a metallic split-ring terahertz (THz) electromagnetic resonator. Moiré superlattice embedded in a THz resonator is a suitable system to explore cavity control at frequency down to the Terahertz range. Here we study the topological transition in cavity-embedded moiré superlattice doped at filling factor 1 (one electron/hole per supercell). Within the mean-field approximation, we show that the virtual-photon-mediated interaction can introduce a topological band inversion, namely the electronic system can be in the topological trivial (nontrivial) states in the absence (presence) of the cavity in a vacuum. The cavity vacuum-mediated interaction Hamiltonian provides a topological nontrivial mass term, which is also gate-tunable. Our results point to a promising new toolbox for manipulating topological transition.