Anomalous Exciton-Condensation in Graphene Bilayers

In ordinary semiconductor bilayers, exciton condensates appear at total Landau level filling factor ${\nu }_T=1$. We predict that similar states will occur in Bernal stacked graphene bilayers at many non-zero integer filling factors. For ${\nu }_T=-3,1$ we find that the superfluid density of the exciton condensate vanishes and that a finite-temperature fluctuation induced first order isotropic-smectic phase transition occurs when the layer densities are not balanced. These anomalous properties of bilayer graphene exciton condensates are due to the degeneracy of Landau levels with $n=0$ and $n=1$ orbital character.