Ordered states in AB bilayer graphene in a SU(4)-symmetric model

We apply SU(4)-symmetric model to examine possible ordered states in AB-stacked bilayer graphene (AB-BLG). The Hamiltonian of the system possesses this symmetry under certain assumptions. In such a model the multicomponent order parameter can be presented as a $4\ifmmode\times\else\texttimes\fi{}4$ matrix $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Q}$. Using a mean-field approximation, we derive a self-consistency equation for $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Q}$. Among possible solutions of the obtained equation there are anomalous quantum Hall states, spin, charge, spin-valley density waves, interlayer excitonic phases, and their combinations. We argue that the proposed approach is a useful tool for classification of the ordered states in AB-BLG. The ordered states of the SU(4)-symmetric model demonstrate extensive degeneracies. The degeneracies can be removed by taking into account the neglected non-SU(4)-symmetric terms, disorder, substrate, as well as other perturbations. The ordered states have varying sensitivity to these factors. This suggests that, for AB-BLG, a ground-state ordering type is a nonuniversal property, susceptible to particulars of extrinsic conditions.