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We propose a generic topological insulator bilayer (TIB) system to study theexcitonic condensation with self-consistent mean-field (SCMF) theory. We showthat the TIB system presents the crossover behavior from theBardeen-Cooper-Schrieffer (BCS) limit to Bose-Einstein condensation (BEC)limit. Moreover, by comparison with traditional semiconductor systems, we findthat for the present system the superfluid property in the BEC phase is moresensitive to electron-hole density imbalance and the BCS phase is more robust.Applying this TIB model into Bi$_{2}$Se$_{3}$-family material, we find that theBEC phase is most probable to be observed in experiment. We also calculate thecritical temperature for Bi$_{2}$Se$_{3}$-family TIB system, which is$\mathtt{\sim}100$ K. More interestingly, we can expect this relativehigh-temperature excitonic condensation since our calculated SCMF criticaltemperature is approximately equal to the Kosterlitz-Thouless transitiontemperature.

Excitonic condensation for the surface states of topological insulator bilayers