Quadriexcitons and excitonic condensate in a symmetric electron-hole bilayer with valley degeneracy

Using quantum Monte Carlo simulations we have mapped out the zero-temperature phase diagram of a symmetric electron-hole bilayer with twofold valley degeneracy, as a function of the interlayer distance d and in-layer density n. We find that the effect of the valley degeneracy is to shrink the region of stability of the excitonic condensate, in favor of quadriexcitons at small d and of the four-component plasma at large d, with minor effects on the value of the excitonic condensate fraction. The enclosure of the condensate in a density window possibly explains why anomalous tunneling conductivity, interpreted as a signature of condensation, is observed only between two finite values of carrier density in graphene bilayers. Our phase diagram may provide directions to select device parameters for future experiments.