Excitonic condensation for the surface states of topological insulator bilayers

We propose a generic topological insulator bilayer (TIB) system to study the excitonic condensation with self-consistent mean-field (SCMF) theory. We show that the TIB system presents the crossover behavior from the Bardeen–Cooper–Schrieffer (BCS) limit to the Bose–Einstein condensation (BEC) limit. Moreover, in comparison with traditional semiconductor systems, we find that for the present system the superfluid property in the BEC phase is more sensitive to electron–hole density imbalance and the BCS phase is more robust. Applying this TIB model to the Bi2Se3-family material, we find that the BEC phase is most likely to be observed in experiment. We also calculate the critical temperature for the Bi2Se3-family TIB system, which is ∼100 K. More interestingly, one can expect this relative high-temperature excitonic condensation, since our calculated SCMF critical temperature is approximately equal to the Kosterlitz–Thouless transition temperature.