Multicomponent electron-hole superfluidity and the BCS-BEC crossover in double bilayer graphene

Superfluidity in coupled electron-hole sheets of bilayer graphene is predicted here to be multicomponent because of the conduction and valence bands. We investigate the superfluid crossover properties as functions of the tunable carrier densities and the tunable energy band gap $E_g$. For small band gaps there is a significant boost in the two superfluid gaps, but the interaction driven excitations from the valence to the conduction band can weaken the superfluidity, even blocking the system from entering the BEC regime at low densities. At a given larger density, a band gap $E_g\sim 40$-$60$ meV can carry the system into the strong-pairing multiband BCS-BEC crossover regime, the optimal range for realization of high-$T_c$ superfluidity.