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Superfluidity has recently been reported in double electron-hole bilayergraphene. The multiband nature of the bilayers is important because of the verysmall band gaps between conduction and valence bands. The long range nature ofthe superfluid pairing interaction means that screening must be fully takeninto account. We have carried out a systematic mean-field investigation thatincludes (i) contributions to screening from both intraband and interbandexcitations, (ii) the low-energy band structure of bilayer graphene with itssmall band gap and flattened Mexican hat-like low-energy bands, (iii) the largedensity of states at the bottom of the bands, (iv) electron-hole pairing in themultibands, and (v) electron-hole pair transfers between the conduction andvalence band condensates. We find that the superfluidity strongly modifies theintraband contributions to the screening, but that the interband contributionsare unaffected. Unexpectedly, the net effect of the screening is to suppressJosephson-like pair transfers and to confine the superfluid pairing entirely tothe conduction band condensate even for very small band gaps, making the systembehave similarly to a one-band superfluid.

Multicomponent screening and superfluidity in gapped electron-hole double bilayer graphene with realistic bands