Interedge van der Waals interaction between two-dimensional materials

Interedge van der Waals interactions between coplanar two-dimensional metals or semimetals are investigated via the coupled-plasmon approach and many-body dispersion theory. Unlike the ``standard'' power law $E\ensuremath{\sim}{d}^{\ensuremath{-}3}$ derived from pairwise theory, the nonretarded zero-point energy does not scale with interedge distance as a power law, with the slope of the ln(\ensuremath{-}$E$)-ln($d$) relation changing from $\ensuremath{\sim}\ensuremath{-}1$ at $2\phantom{\rule{0.16em}{0ex}}\AA{}$ to $\ensuremath{\sim}\ensuremath{-}3$ at $10\phantom{\rule{0.16em}{0ex}}\AA{}$. The attractive force for two 10 nm long parallel edges of graphene separated by $4\phantom{\rule{0.16em}{0ex}}\AA{}$ can be up to 6.8 nN, implying that the interedge dispersion force at subnanometer separations might be experimentally detectable. We further show that the interaction can be partly screened by dielectric environments, with the strength of screening being sensitive to whether both surfaces are covered and decaying with the interlayer separation from dielectric substrates.