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

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