Screened potential of a test charge in a two-dimensional Bose condensate

We calculate the screening properties of a boson superlattice with distanced between the planes at temperature zero. The screened Coulomb potentialV_s(r,d) of a test charge located in one plane is calculated in the neighboring plane. It is found that this interplane potential is attractive with a maximal atraction at the intraplane distancer_m:V_s(r_m,d)<0.V_s(r_m,d) versusd shows a minimum atd_m, indicating a maximal attraction for anoptimal superlattice period d_m. The attraction could give rise topairing of bosons between different planes.