Universal tuning of quantum electrodynamic interactions from power laws to exponential screening and logarithmic antiscreening

We introduce a material-agnostic platform for \emph{universal tuning of quantum electrodynamic interactions from power laws to exponential screening and logarithmic antiscreening}, realized in a dielectric spacer bounded by two gate-tunable two-dimensional conductors. The structured electromagnetic environment is completely specified by the transverse-magnetic and transverse-electric reflection amplitudes $r_{\mathrm{TM/TE}}(q_\perp,\omega)$ of the sheets. Starting from the QED action and a Green-function formulation, we resum the multiple-reflection series and show that the interactions are governed by a discrete set of transverse cavity harmonics. In the transparent limit $r_{\rm TM}\to 0$, the interactions reduce to bulk power laws $U(\rho)\propto \rho^{-\alpha}$. In the reflective limit $|r_{\rm TM}|\to 1$, the \emph{phase/parity} of $r_{\rm TM}$ selects two qualitatively distinct branches: a Dirichlet/PEC (screening) branch $r_{\rm TM}\to -1$ that removes the gapless transverse mode and yields an evanescent Bessel-$K$ function $U(\rho)\propto e^{-\pi\rho/d}/\sqrt{\rho/d}$ at $\rho\gg d$, and an opposite Neumann/PMC-like (antiscreening) branch $r_{\rm TM}\to +1$ that retains a gapless mode and can strongly enhance the long-range tail. Thus, the same heterostructure provides in situ electrical control over both the \emph{range} and the \emph{strength} of mediated interactions.