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

Abstract

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 \(r_{\mathrm{TM/TE}}(q_\perp,ω)\) 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 \(U(ρ)\propto ρ^{-α}\). 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 \(U(ρ)\propto e^{-πρ/d}/\sqrt{ρ/d}\) at \(ρ\gg d\), 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.

Figures (2)

• Figure 1: Universal tuning of interaction range, screening, and logarithmic antiscreening.(a) Conductor--dielectric--conductor heterostructure: a dielectric spacer of thickness $d$ bounded by two gate-tunable 2D conductors. Two localized objects (here illustrated as spins) reside in the midplane and are separated by a lateral distance $\rho$; shaded profiles schematically indicate how the interaction can be reprogrammed by changing the electromagnetic boundary conditions. (b) Gate tuning of the TM boundary response and the resulting asymptotic envelopes. Left: representative magnitude of the static TM reflection amplitude $|r_{\rm TM}|$ for a graphene-based sheet model as a function of carrier density $n$, illustrating continuous electrical tuning from a nearly transparent regime ($|r_{\rm TM}|\!\ll\!1$) toward a strongly reflecting regime ($|r_{\rm TM}|\!\to\!1$). Right: corresponding midplane interaction envelopes versus reduced distance $x=\rho/d$, showing three universal regimes: a bulk-like ON power law ($x^{-\alpha}$); exponential screening in the Dirichlet/PEC parity branch ($r_{\rm TM}\to -1$), governed by the modified Bessel function $K_0(\pi x)$; and a quasi-two-dimensional logarithmic antiscreening regime in the opposite parity branch ($r_{\rm TM}\to 1^{-}$), $\mathcal{D}_F(\rho;0)\propto (1/d)\ln(\rho_\ast/\rho)$ for $d\ll \rho \ll \rho_\ast$ with $\rho_\ast\sim d/(1-r_{\rm TM})$ (see Sec. \ref{['sec:SI_quasi-2D_log']}). (c) Ladder (non-crossing) two-photon exchange diagram in the linked-cluster expansion for the fluctuation-induced interaction: two local response vertices (polarizabilities $\alpha$ for vdW/CP, or QED--DSR spin--electric vertices $\tfrac{1}{2}\,\sigma\!\cdot\!\beta$) are connected by two cavity photon propagators $\mathbb D_{12}(i\xi_m)$ and $\mathbb D_{21}(i\xi_m)$, yielding the leading connected contribution $\propto \mathrm{Tr}[\mathbb T_1\mathbb D_{12}\mathbb T_2\mathbb D_{21}]$ at Matsubara frequency $\xi_m$. (d) Crossed-ladder two-photon exchange diagram, obtained by exchanging the two photon lines. Together with panel c it represents the two distinct covariant topologies of two-photon exchange (capturing all time orderings in the linked-cluster/Matsubara formulation), and underlies the compact second-order free-energy used in the main text and SI for vdW/CP and QED--DSR exchange.
• Figure 2: Tunable interaction range and strength controlled by the TM reflection amplitude. Normalized interactions versus reduced distance $x=\rho/d$ for representative values of the TM reflection amplitude $r_{\rm TM}$ (legend), illustrating continuous tuning between bulk-like power laws (transparent/ON limit $r_{\rm TM}\!\approx\!0$) and strongly modified long-range behavior for reflective mirrors ($|r_{\rm TM}|\!\approx\!1$). (a) Static Coulomb interaction $U/U_{\rm on}$. (b) Static electric dipole--dipole interaction $U_{dd}/U_{dd,\rm on}$ (computed from the second derivative of the scalar propagator; in-plane proxy). (c) Fluctuation-induced vdW/CP interaction shown as a proxy proportional to the squared dipolar Feynman propagator (capturing the characteristic $\mathbb{D}\mathbb{D}$ dependence). (d) QED-DSR-mediated spin--spin exchange shown as a proxy proportional to the squared Coulomb interaction (capturing the characteristic $\mathbb{D}\mathbb{D}$ dependence in the TM-dominant $E_z$-coupled case). For $|r_{\rm TM}|\ll 1$, curves are evaluated using the rapidly convergent image-lattice (power-law) representation; for $|r_{\rm TM}|\approx 1$, curves are evaluated using the Poisson/Schwinger representation (Bessel-harmonic function with the exact $\Delta S$ correction computed from the $\mathrm{erfc}$ / $\mathrm{erfcx}$ form). The sign of $r_{\rm TM}$ selects screening (Dirichlet/PEC branch $r_{\rm TM}\to -1$) versus antiscreening (Neumann/PMC-like branch $r_{\rm TM}\to +1$), corresponding to alternating versus same-sign image parity. For $r_{\rm TM}\to 1^-$, the surviving $\ell=0$ sector produces a quasi-2D logarithmic Feynman propagator $\mathcal{D}_F(\rho;0)\propto (1/d)\ln(\rho_\ast/\rho)$ over $d\ll\rho\ll\rho_\ast$ with $\rho_\ast\sim d/(1-r_{\rm TM})$, which explains the large enhancements at $x\sim 10^2\!-\!10^3$ for $r_{\rm TM}=0.99$ and $0.9999$ (Sec. \ref{['sec:SI_quasi-2D_log']}). See Sec. \ref{['sec:SI_num_Fig2']} for the exact analytic expressions (including the $\mathop{\mathrm{erfcx}}\nolimits$ form) and numerical evaluation method used to generate the curves.