Competing charge-density-wave, magnetic and topological ground states at and near Dirac points in graphene in axial magnetic fields

In the presence of axial magnetic fields that can be realized in deliberately buckled monolayer graphene, quasi-relativistic Dirac fermions may find themselves in a variety of broken symmetry phases even for weak interactions. Through a detailed Hartree self-consistent numerical calculation in finite strained graphene with cylindrical and open boundaries we establish the possibility of realizing a charge-density-wave order for the spinless fermions in the presence of weak nearest-neighbor repulsion. Such an instability gives rise to a staggered pattern of average fermionic density between bulk and boundary of the system as well as among two sublattices of graphene, due to the spatial separation of the zero energy states localized on opposite sublattices. Although with fermions spin restored, an unconventional magnetic order driven by the onsite repulsion, possibly leads to the dominant instability at the Dirac point, the proposed charge-density-wave order can nevertheless be realized at finite doping, which is always accompanied by a finite ferromagnetic moment. Additionally, the charge-density-wave phase supports a quantized charge or spin Hall conductivity when its formation away from the Dirac point is further preceded by the appearance of topological anomalous or spin Hall insulator respectively. The topological orders in strained graphene can be supported by weak second neighbor repulsion, for example. Therefore, depending on the relative strength of various short-range components of the Coulomb interaction a number of broken symmetry phases can be realized within the zero energy manifold in strained graphene.