Exciton condensation in biased bilayer graphene

We consider suspened bilayer graphene under applied perpendicular electric bias field that is known to generate a single particle gap $2Δ$ and a related electric polarization ${\cal P}$. We argue that the bias also drives a quantum phase transition from band insulator to superfluid exciton condensate. The transition occurs when the exciton binding energy exceeds the band gap $2Δ$. We predict the critical bias (converted to band gap), $Δ_c\approx 60$ meV, below which the excitons condense. The critical temperature, $T_c(Δ)$, is maximum at $Δ\approx 25$ meV, $T_c^\text{max}\approx 115$ K, decreasing significantly at smaller $Δ$ due to thermal screening. Entering the condensate phase, the superfluid transition is accompanied by a cusp in the electric polarization ${\cal P}(Δ)$ at $Δ\toΔ_c$, which provides a striking testable signature. Additionally, we find that the condensate prefers to form a pair density wave.

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