Phase diagram of the lowest Landau level in bilayer graphene

Abstract

Broken-symmetry quantum Hall (QH) states with filling factors ν = 0, ±1,±2,±3 in the lowest Landau level in bilayer graphene are analyzed by solving the gap equation in the random phase approximation. It is shown that in the plane of electric and magnetic fields, the critical line, which separates the spin and layer polarized phases at ν = 0, extends to the ν = ±1 QH states. The amplitudes of the gaps in the ν = ±1,±3, and ν = ±2 QH states are significantly smaller than the amplitude of the ν = 0 gap, due to the separate filling of the n = 0 and n = 1 orbital Landau levels and the negative contribution of the Hartree term, respectively. It is shown that those values of the external electric field where the conductance is not quantized correspond to the minima of the gaps.