Asymmetric bandgaps and Landau levels in a Bernal-stacked hexagonal boron-nitride bilayer

A Bernal-stacked hexagonal boron-nitride (h-BN) bilayer is a two-dimensional polar crystal. Within the tight-binding approximation, we investigate the band structure of a gated h-BN bilayer by analyzing the density of states and the behavior of the charge transfer. We find that the bandgaps of the h-BN bilayer vary asymmetrically under two opposite biases due to asymmetric changes of the interlayer and intralayer polarities. We also find that the bias-driven net charge transfer between layers can be up to 0.2 electron per unit cell. Under the bias along one direction, the system exhibits quantum phase transitions from a semiconductor to a semimetal and then to a semiconductor again, whereas under the reverse bias, the system is always semiconducting. Besides, asymmetric Landau levels under opposite biases arise in the presence of a magnetic field. Moreover, dispersive edge states are found to exist in the bulk bandgap for an h-BN bilayer nanoribbon under the bias along one direction, which does not happen when the bias is reversed. All these properties of h-BN bilayers are measurable in transport experiments.