The realization of systems of spatially separated electrons and holes, in the search of the equilibrium excitonic condensate foreseen by , has gone on for more than two decades, but so far the condensate has eluded experimental detection . It has been recently suggested that a substantial enhancement of the electron-hole attraction, to favour the condensate, could be obtained in coupled graphene bilayers ; a couple of experimental realizations has promptly followed . Such systems have a quadratic energy dispersion on a wide density range and a twofold valley degeneracy in each bilayer.
We have performed calculations for an electron-hole bilayer with mass symmetry and twofold valley degeneracy (in each layer), to partially mimic the situation encountered in the coupled graphene bilayers proposed in . Our goal is to provide estimates of the pairing gap for the electron-hole bilayer investigating the qualitative and quantitative effects of the valley degeneracy.
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 See, e.g., J. A. Seamons et al., Phys. Rev. Lett. 102, 026804 (2009) and references therein.
 A. Perali, D. Neilson, and A. R. Hamilton, Phys. Rev. Lett. 110, 146803 (2013).
 J. I. A. Li, T. Taniguchiet al.,Phys. Rev. Lett. 117, 046802 (2016); K. Lee et al.,Phys. Rev. Lett. 117, 046803 (2016).