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 similar to 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.