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Cooper pairing of spatially separated electrons and holes in graphene bilayeris studied beyond the mean-field approximation. Suppression of the screening atlarge distances, caused by appearance of the gap, is consideredself-consistently. A mutual positive feedback between appearance of the gap andenlargement of the interaction leads to a sharp transition to correlated statewith greatly increased gap above some critical value of the coupling strength.At coupling strength below the critical, this correlation effect increases thegap approximately by a factor of two. The maximal coupling strength achievablein experiments is close to the critical value. This indicated importance ofcorrelation effects in closely-spaced graphene bilayers at weak substratedielectric screening. Another effect beyond mean-field approximation consideredis an influence of vertex corrections on the pairing, which is shown to be veryweak.

Cooper pairing of electrons and holes in graphene bilayer: Correlation effects