A variational method in the problem of screening an external charge in   strongly correlated metals
  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. 
G.G. Guzm\'an-Verri, Arkady Shekhter, and C.M. Varma
cond-mat.str-el