the distance of the vacuum gap. $\gamma = \sqrt{k_x^2+k_y^2} $. The drifted reflection coefficient is computed according to $r_1= v_{{\bf k}_\perp} \Pi(\omega, {\bf k}_\perp, v_1) / \bigl[1-  v_{{\bf k}_\perp} \Pi(\omega, {\bf k}_\perp, v_1)\bigr]$. The bare Coulomb interaction in wavevector space in two dimensions is $v_{{\bf k}_\perp} = 1/(2\epsilon_0 \gamma)$. $r_2$ is computed at no drift ($v_1=0$). We calculate the drifted polarization function following the approximation of Svintsov et al.[@svintsov18]: $$\begin{aligned}
\Pi_{{\bf k}_\perp}(\omega, v_1) &=& 
\frac{e^2 \mu(T_i)}{ (\pi \hbar v_F)^2} \int_0^{2\pi}\! d\theta\, 
\frac{1}{(1 - \beta \cos\theta)^2}\times \qquad \nonumber \\
&&  \frac{ k_x (\cos\theta - \beta) + k_y \sin\theta}{ (\hbar \omega + i \eta)/(\hbar v_F)
- k_x \cos\theta - k_y \sin\theta},\quad\end{aligned}$$ where we define $\beta = v_1/v_F$, the Fermi velocity is $v_F = \frac{3}{2} a t/\hbar$ with carbon bond length $a = 1.42\,$Å and hopping parameter $t=2.8\,$eV, and $\eta$ is a small electron damping parameter, which gives graphene a finite DC conductivity. Finally, $\mu(T) = 2 k_b T \ln [ 2\cosh\frac{\mu}{2 k_b T} ]$. The long-wave approximation (${\bf k}_\perp$ small) is valid as the contribution of the transmission is concentrated around $\gamma \sim O(1/d)$. The appendices further discuss details of the approximations and calculations.

![ (a) Integrated spectral transfer function $f(\omega)$ as 