Topological insulators in strained graphene at weak interaction

The nature of the electronic ground states in strained undoped graphene at weak interaction between electrons is discussed. After providing a lattice realization of the strain-induced axial magnetic field we numerically find the self-consistent solution for the time reversal symmetry breaking quantum anomalous Hall order parameter, at weak second-nearest-neighbor repulsion between spinless fermions. The anomalous Hall state is obtained in both uniform and nonuniform axial magnetic fields, with the spatial profile of the order parameter resembling that of the axial field itself. When the electron spin is included, the time reversal symmetric anomalous spin Hall state becomes slightly preferred energetically at half filling, but the additional anomalous Hall component should develop at a finite doping.