Tuning Topologically Nontrivial States in the BHT-Ni Metal-Organic Framework.

Using first-principles calculations, we have demonstrated the creation of multiple quantum states in the experimentally accessible metal-organic framework BHT-Ni. Specifically, quantum spin Hall and quantum anomalous Hall states are induced by two- and four-electron doping, respectively. Geometrical symmetry breaking is also investigated in cis- and trans-like structures. For a low electron doping concentration of two electrons per unit cell, the Fermi energy shifts to a nontrivial band gap between the Dirac bands, predicting a quantized spin Hall conductivity. Subsequently at a high electron doping concentration, an anomalous Hall conductivity with a quantized value is observed. In addition, for a centrosymmetric (trans-like) structure, it preserves the quantum spin Hall state and quantized spin Hall conductivity. In contrast, in the noncentrosymmetric (cis-like) structure, the breaking of space inversion symmetry leads to the emergence of the valley Hall effect and the disappearance of spin Hall conductivity.