Possible broken inversion and time-reversal symmetry state of electrons in bilayer graphene

Abstract

With the two-band continuum model, we study the broken inversion and time-reversal symmetry state of electrons with finite-range repulsive interactions in bilayer graphene. In the state, there are overlapped loop currents in each layer. With the analytical solution to the mean-field Hamiltonian, we obtain the electronic spectra. The ground state is gapped. In the presence of the magnetic field $B$, the energy gap grows with increasing $B$, in excellent agreement with the experimental observation. Such an energy-gap behavior originates from the disappearance of a Landau level of $n=0$ and 1 states. The present result resolves explicitly the puzzle of the gap dependence of $B$.