The recently synthesized silicene as well as theoretically discussed germanene are examples of buckled honeycomb structures. The buckled structures allow one to manipulate asymmetry between two underlying sublattices of honeycomb structures. Here by taking germanene as a prototype of buckled honeycomb lattices, we explore magnetism induced by breaking sublattice symmetry through saturating chemical bonds on one-side of the buckled honeycomb lattice. It is shown that when fractions of chemical bonds on one-side are saturated, two narrow bands always exist at half filling. Furthermore, the narrow bands generally support flat band ferromagnetism in the presence of the Hubbard U interaction. The induced magnetization is directly related to the saturation fraction and is thus controllable in magnitude through the saturation fraction. Most importantly, we find that depending on the saturation fraction, the ground state of an one-side saturated germanene may become a quantum anomalous Hall (QAH) insulator characterized by a Chern number that vanishes for larger magnetization. The non-vanishing Chern number for smaller magnetization implies that the associated quantum Hall effect tends to survive at high temperatures. Our findings provide a potential method to engineer buckled honeycomb structures into high-temperature QAH insulators.

Although topological insulators (TIs) are known to be robust against non-magnetic perturbations and exhibit edge or surface states as their distinct feature, experimentally it is known that vacancies often occur in these materials and impose strong perturbations. Here we investigate effects of vacancies on the stability of Z2 topological order using the Kane-Mele (KM) model as a prototype of topological insulator. It is shown that even though a vacancy is not classified as a topological defect in KM model, it generally induces a pair of degenerate midgap states only in the TI phase. We show that these midgap states results from edge states that fit into vacancies and are characterized by the same Z2 topological order. Furthermore, in the presence of many vacancies, an impurity band that is degenerate with edge states in energy is induced and mixes directly with edge states. However, the Z2 topological order persists and edge states exist between the impurity band and perturbed bulk bands until a phase transition occurs when Dirac cones near Dirac points are depleted. Our analyses indicate that the same scenario holds for point vacancies or line of vacancies in 3D TIs as well.

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