  Bilayer graphene (BLG) at the charge neutrality point (CNP) is strongly
susceptible to electronic interactions, and expected to undergo a phase
transition into a state with spontaneous broken symmetries. By systematically
investigating a large number of singly- and doubly-gated bilayer graphene (BLG)
devices, we show that an insulating state appears only in devices with high
mobility and low extrinsic doping. This insulating state has an associated
transition temperature Tc~5K and an energy gap of ~3 meV, thus strongly
suggesting a gapped broken symmetry state that is destroyed by very weak
disorder. The transition to the intrinsic broken symmetry state can be tuned by
disorder, out-of-plane electric field, or carrier density.
