We describe a variational calculation for the problem of screening of a point charge in a layered correlated metal for dopings close to the Mott transition where the screening is non-linear due to the proximity to the incompressible insulating state.
We find that external charge can induce locally incompressible regions and that the non-linear dependence of the screening on density can induce overscreening in the nearest nearby layers while preserving overall charge neutrality.
