Inhomogenous electronic structure, transport gap, and percolation threshold in disordered bilayer graphene

The inhomogenous real-space electronic structure of gapless and gapped disordered bilayer graphene is calculated in the presence of quenched charge impurities. For gapped bilayer graphene we find that for current experimental conditions the amplitude of the fluctuations of the screened disorder potential is of the order of (or often larger than) the intrinsic gap $\Delta$ induced by the application of a perpendicular electric field. We calculate the crossover chemical potential, $\Delta_{\rm cr}$, separating the insulating regime from a percolative regime in which less than half of the area of the bilayer graphene sample is insulating. We find that most of the current experiments are in the percolative regime with $\Delta_{\rm cr}<<\Delta$. The huge suppression of $\Delta_{\rm cr}$ compared with $\Delta$ provides a possible explanation for the large difference between the theoretical band gap $\Delta$ and the experimentally extracted transport gap.