At the charge neutrality point, bilayer graphene (BLG) is strongly susceptible to electronic interactions and is expected to undergo a phase transition to a state with spontaneously broken symmetries. By systematically investigating a large number of single-and double-gated BLG devices, we observe a bimodal distribution of minimum conductivities at the charge neutrality point. Although σ min is often approximately 2-3 e 2 ∕h (where e is the electron charge and h is Planck's constant), it is several orders of magnitude smaller in BLG devices that have both high mobility and low extrinsic doping. The insulating state in the latter samples appears below a transition temperature T c of approximately 5 K and has a T ¼ 0 energy gap of approximately 3 meV. Transitions between these different states can be tuned by adjusting disorder or carrier density.topological states | anomalous hall | spontaneous quantum Hall states | electron-electron interactions | layer antiferromagnets B ilayer graphene (BLG) has provided a fascinating new platform for both post-silicon electronics and exotic many-body physics (1-23). Because its conduction and valence bands touch at two points in momentum space and have approximately quadratic dispersion accompanied by momentum-space pseudospin textures with vorticity J ¼ 2, charge-neutral BLG is likely to have a broken-symmetry ground state in the absence of disorder (6-11, 15-18, 24-26). Theoretical work on the character of the ground state in neutral BLG has examined a variety of distinct but related pseudospin ferromagnet states-including gapped anomalous Hall (5,6,19),[16][17][18]22), and current loop states (26)-that break time-reversal symmetry, and gapless nematic states, which alter Dirac point structure and reduce rotational symmetry (6-11, 15-18, 24, 25). The pseudospin degree of freedom reflects the presence of two low-energy carbon sites per unit cell that are localized in different layers. Experimental work has confirmed the strong role of interactions, but has been equivocal in specifying ground-state properties. In particular, both gapped and gapless states have been reported (19-23) in suspended BLG. The low-temperature minimum conductivity at the charge neutrality point (CNP), σ min , has ranged from approximately 0.05 to 250 μS. These orders-of-magnitude differences between σ min values measured in apparently similar samples have been baffling.In this paper we attempt to shed light on these ambiguous findings by systematically examining a large number of single-and double-gated BLG samples, with mobility values ranging from 500 to 2;000 cm 2 ∕V·s for substrate-supported samples and 6,000 to 350,000 for suspended samples. We find a surprisingly constant σ min value of approximately 2-3 e 2 ∕h for a majority of the devices (here, e is the electron charge and h is Planck's constant), independent of their mobility and of the presence or absence of substrates. However, for T below approximately 5 K, the best devices form an insulating state with an energy gap of approximately 2-3...