Tunable energy gap and the transitions between the insulating phases in dual-gated hBN/bilayer graphene superlattices at the charge neutrality point*

We report on the transport properties in hexagonal boron nitride (hBN)/bilayer graphene (BLG) moiré superlattice devices with top and bottom gates (dual gate) enabling individual modulation of the electric displacement field and the carrier density. By measuring the temperature and displacement field dependence of the resistivity at the charge neutrality point (CNP), we estimate the energy gap and demonstrate its tuning by the electric field. Even without an electric field, the alignment of BLG with hBN harbors an energy gap of ~1.4 meV in our device. It is found that the temperature dependence of the resistivity at moiré-induced satellite points is insensitive to an electric field, in contrast to that at the CNP. Under a perpendicular magnetic field, transitions between two insulating phases at the CNP are detected. In the phase diagram, there is no signature of a continuously vanishing gap even in the vicinity of the criticality. This result agrees with a scenario of the formation of a microscopic network of the two competing phases at the first-order transition.