Spontaneous Symmetry Breaking of Cavity Vacuum and Emergent Gyrotropic Effects in Embedded moiré Superlattices

In an electronic system, spontaneous symmetry breaking can arise from many-body interaction between electrons, leading to degenerate ground states distinguishable by emergent effects otherwise prohibited by the symmetry. Here we show that ultrastrong coupling of a mesoscopic electronic system to the vacuum of a cavity resonator can lead to another paradigm of spontaneous breaking of spatial symmetries in both systems. As a pertinent example, we consider the orbital gyrotropic effects in a moiré superlattice embedded in a THz split ring cavity resonator. Our mean-field and exact diagonalization calculations consistently demonstrate a spontaneous parity symmetry breaking in both the electronic ground state and the cavity vacuum, leading to two degenerate hybrid ground states distinguished by their opposite orbital gyrotropic Hall and magnetic effects. These sizable responses in the cavity-embedded moiré superlattice are highly tunable by both the cavity field polarization and interlayer bias on the moiré superlattice, providing an advanced platform for manipulating gyrotropic effects.