Combining tight-binding (TB) models with first-principles calculations, we investigate electronic and topological properties of plumbene. Different from the other two-dimensional (2D) topologically nontrivial insulators in group IVA (from graphene to stanene), low-buckled plumbene is a topologically trivial insulator. The plumbene without spin-orbit coupling exhibits simultaneously two kinds of degeneracies, i.e., quadratic non-Dirac and linear Dirac band dispersions around the Gamma and K/K points, respectively. Our TB model calculations show that it is the coupling between the two topological states around the Gamma and K/K points that triggers the global topologically trivial property of plumbene. Quantum anomalous Hall effects with Chern numbers of 2 or -2 can be, however, achieved after an exchange field is introduced. When the plumbene is functionalized with ethynyl (PbC2H), quantum spin Hall effects appear due to the breaking of the coupling effect of the local topological states.
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