  We study anisotropic (patchy) screening induced by the resonant conversion of
cosmic microwave background (CMB) photons into dark-sector massive vector
bosons (dark photons) as they cross non-linear large scale structure (LSS).
Resonant conversion takes place through the kinetic mixing of the photon with
the dark photon, one of the simplest low energy extensions to the Standard
Model. In the early Universe, resonant conversion can occur when the photon
plasma mass, obtained as the photon propagates through the ionized interstellar
and intergalactic media, matches the dark photon mass. After the epoch of
reionization, resonant conversion occurs mainly in the ionized gas that
occupies virialized dark matter halos, for a range of dark photon masses
between $10^{-13} {\rm \; eV} \lesssim m_{{\rm A^{\prime}}} \lesssim 10^{-11}
{\rm \; eV}$. This leads to new CMB anisotropies that are correlated with LSS,
which we refer to as patchy dark screening, in analogy with anisotropies from
Thomson screening. Its unique frequency dependence allows it to be
distinguished from the blackbody CMB. In this paper, we use a halo model
approach to predict the imprint of dark screening on the CMB temperature and
polarization anisotropies, as well as their correlation with LSS. We then
examine the two- and three-point correlation functions of the dark-screened
CMB, as well as correlation functions between CMB and LSS observables, to
project the sensitivity of future measurements to the kinetic mixing parameter
and dark photon mass. We demonstrate that an analysis with existing CMB data
can improve upon current constraints on the kinetic mixing parameter by two
orders of magnitude with the two-point correlation functions, while data from
upcoming CMB experiments and LSS surveys can further improve the reach by
another order of magnitude with two- and three-point correlation functions.
