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.
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