Electron screening and excitonic condensation in double-layer graphene systems

We theoretically investigate the possibility of excitonic condensation in a system of two graphene monolayers separated by an insulator in which electrons and holes in the layers are induced by external gates. In contrast to the recent studies of this system, we take into account the screening of the interlayer Coulomb interaction by the carriers in the layers, and this drastically changes the result. Due to a large number of electron species in the system (two projections of spin, two valleys, and two layers) and to the suppression of backscattering in graphene, the maximum possible strength of the screened Coulomb interaction appears to be quite small, making the weak-coupling treatment applicable. We calculate the mean-field transition temperature for a clean system and demonstrate that its highest possible value T-c(max)similar to 10(-7)epsilon(F)less than or similar to 1 mK is extremely small (epsilon(F) is the Fermi energy). In addition, any sufficiently short-range disorder with the scattering time tau less than or similar to h/T-c(max) would suppress the condensate completely. Our findings render experimental observation of excitonic condensation in the above setup improbable even at very low temperatures.