First-principles investigations on the Berry phase effect in spin-orbit coupling materials

In recent years, the Berry phase as a fascinating concept has made a great success for interpreting many physical phenomena. In this paper, we review our past works on the Berry phase effect in solid materials with spin-orbit coupling. Firstly, we developed an exact method for directly evaluating the Berry curvature and anomalous Hall conductivity, then the intrinsic mechanism of anomalous Hall effect was quantitatively confirmed in bcc Fe and CuCr₂Se_4-xBr_x. An effective method was proposed to decompose the anomalous Hall effect into the intrinsic and extrinsic contributions. We also developed computational methods for the spin Hall conductivity and anomalous Nernst conductivity. Secondly, we developed a powerful method for computing the Z₂ topological invariant without consideration of special symmetry. We predicted many topological insulators in three-dimensions, including half-Heusler, chalcopyrite, strained InSb, core-holed Ge and InSb, Bi₂Te₃/BiTeI heterostructure, and in two-dimensions, including silicene, germanene, stanene, X-hydride/halide (X = N-Bi) monolayers and Bi₄Br₄. We also predicted the quantum anomalous Hall effect in magnetic atoms adsorbed graphene and half-passivated BiH, the quantum valley Hall effect and topological superconducting in silicene and n-dopped BiH. Finally, the summary of our past works and the further outlooks are discussed.