Cavity Tuning of the CDW--Superconductivity Interplay in a Kagome Metal
Kagome metals host competing electronic orders, including charge-density-wave (CDW) order and superconductivity, shaped by intertwined lattice, electronic-correlation, and kagome-geometric effects. Here, using quantum electrodynamical density functional theory, we identify an equilibrium cavity route for reshaping this balance in the kagome metal CsV$_3$Sb$_5$. An out-of-plane polarized single-mode cavity selectively softens CDW-related phonons, counteracting pressure-induced hardening and extending the CDW instability toward higher pressures. In the high-pressure regime where the CDW instability is otherwise suppressed, cavity coupling redistributes Eliashberg spectral weight toward lower frequencies, enhances the total electron--phonon coupling (EPC), and increases the EPC-based Allen--Dynes estimate of $T_c$. This response originates from a charge-density redistribution induced by the out-of-plane photon mode, which modifies lattice restoring forces and drives the phonon and EPC renormalization. These results establish cavity quantum electrodynamics as a viable equilibrium route for tuning intertwined charge order, lattice dynamics, and superconductivity in kagome materials.