  The p-n junction has provided the basis for the semiconductor-device
industry. Investigations of p-n junctions based on Mott insulators is still in
its infancy. Layered Mott insulators, such as the cuprates or other transition
metal-oxides, present a special challenge since strong in-plane correlations
are important. Here we model the planes carefully using plaquette Cellular
Dynamical Mean Field Theory with an exact diagonalization solver. The energy
associated with inter-plane hopping is neglected compared with the long-range
Coulomb interaction that we treat in the Hartree-Fock approximation. Within
this new approach, "Dynamical Layer Theory", the charge redistribution is
obtained at the final step from minimization of a function of the layer
fillings. A simple analytical description of the solution, in the spirit of
Thomas-Fermi theory, reproduces quite accurately the numerical results. Various
interesting charge reconstructions can be obtained by varying the Fermi energy
differences between both sides of the junction. One can even obtain quasi-two
dimensional charge carriers at the interface, in the middle of a Mott
insulating layer. The density of states as a function of position does not
follow the simple band bending picture of semiconductors.
