▎ 摘　　要

The pairing of electrons and holes due to their Coulomb attraction in two parallel, independently gated graphene layers separated by a barrier is considered. At a weak coupling, there exists the BCS-like pair-condensed state. Despite the fact that electrons and holes behave like massless Dirac fermions, the problem of BCS-like electron-hole pairing in the graphene bilayer turns out to be rather similar to that in usual coupled semiconductor quantum wells. The distinctions are due to the Berry phase of electronic wavefunctions and different screening properties. We estimate the values of the gap in a one-particle excitation spectrum for different interlayer distances and carrier concentrations. The influence of the disorder is discussed. At a large enough dielectric susceptibility of the surrounding medium, the weak coupling regime holds at arbitrarily small carrier concentrations. Localized electron-hole pairs are absent in graphene, thus the behavior of the system versus the coupling strength is cardinally different from usual BCS-BEC crossover.