  We study the effect of interlayer Coulomb interaction in an electronic double
layer. Assuming that each of the layers consists of a bipartite lattice, a
sufficiently strong interlayer interaction leads to an interlayer pairing of
electrons with a staggered order parameter. We show that the correlated pairing
state is dual to the excitonic pairing state with uniform order parameter in an
electron-hole double layer. The interlayer pairing of electrons leads to strong
current-current correlations between the layers. We also analyze the interlayer
conductivity and the fluctuations of the order parameter, which consists of a
gapped and a gapless mode.
