Cavity control of quantum phase transitions in a two-dimensional kondo lattice

Cavity quantum electrodynamics offers a route to control quantum phases by using vacuum fluctuations of confined electromagnetic fields. In particular, planar cavities based on polar van der Waals materials can generate strongly confined modes and are promising for controlling two-dimensional correlated materials. Recently, moir\'e materials have become central platforms for studying two-dimensional heavy-fermion systems and their quantum phase transitions. Kondo lattices provide a prototypical model for studying quantum phase boundaries, driven by competition between Kondo screening and the ordering of local magnetic moments. We show that a cavity-induced interaction can shift the quantum phase transitions between a heavy-fermion phase and an antiferromagnetic phase in a two-dimensional Kondo lattice through a momentum-dependent self-energy of the conduction bands. For the longitudinal projected field motivated by h-BN hyperbolic phonon polaritons, the self-energy favors Kondo hybridization and expands the heavy-fermion region. Transverse and circular in-plane model structures give distinct effects, with the transverse case relatively favoring the magnetically ordered phase and the circular case lying between the longitudinal and transverse cases. These results indicate that electromagnetic vacuum fluctuations can effectively modify the control parameters of strongly correlated two-dimensional Kondo materials.