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 $r_{\mathrm{T}\mathrm{M}\mathrm{/}\mathrm{T}\mathrm{E}}(q_{\perp },\omega )$ 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 $r_{\mathrm{T}\mathrm{M}}\to 0$, the interactions reduce to bulk power laws $U(\rho )\propto {\rho }^{-\alpha }$. In the reflective limit $\mathrm{\mid }{r}_{\mathrm{T}\mathrm{M}}\mathrm{\mid }\to 1$, the \emph{phase/parity} of $r_{\mathrm{T}\mathrm{M}}$ selects two qualitatively distinct branches: a Dirichlet/PEC (screening) branch $r_{\mathrm{T}\mathrm{M}}\to -1$ that removes the gapless transverse mode and yields an evanescent Bessel-$K$ function $U(\rho )\propto e^{-\pi \rho \mathrm{/}d}\mathrm{/}\sqrt{\rho \mathrm{/}d}$ at $\rho \gg d$, and an opposite Neumann/PMC-like (antiscreening) branch $r_{\mathrm{T}\mathrm{M}}\to +1$ 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.