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Ordered-Current State of Electrons in Bilayer Graphene

Based on the four-band continuum model, we study the ordered-current state (OCS) for electrons in bilayer graphene at the charge neutrality point. The present work resolves the puzzles that (a) the energy gap increases significantly with increasing the magnetic field $B$, (b) the energy gap can be closed by the external electric field of either polarization, and (c) the particle-hole spectrum is asymmetric in the presence of $B$, all these as observed by the experiment. We also present the prediction of the hysteresis energy gap behavior with varying $B$, which explains the existing experimental observation on the electric conductance at weak $B$. The large energy gap of the OCS is shown to originate from the disappearance of Landau levels of $n$ = 0 and 1 states in conduction/valence band. By comparing with the existing models and the experiments, we conclude that the OCS is a possible ground state of electrons in bilayer graphene.