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We investigate the anomalous effects due to the Berry correction and theconsiderable perturbations in the silicene-like hexagonal lattice system. TheBerry curvature in periodic Bloch band system which related to theelectromagnetic field is explored, the induced transverse anomalous velocitygives rise to the intrinsic Hall conductivity (without the vertex correction)expecially in the quantum anomalous Hall phase. The quantum anomalous Halleffect which related to the anomalous velocity term is detected, including theband avoided corssing effect and the generated special band gap. %{EnlargedGalilean symmetry of anyons and the Hall effect} The topological spin transportis affected by the Berry curvature %{Topological spin transport of arelativistic electron} %{Anomalous direction for skyrmion bubble motion} andthe spin-current-induced Skyrmion spin texture motion is contrasted between thequantum spin Hall effect and quantum anomalous Hall effect. Since siliceneinvolving the orbital degree of freedom, the orbital magnetic moment andorbital magnetization contributes significantly to the electronic transportproperties of silicene %{Photoinduced quantum spin and valley Hall effects, andorbital magnetization in monolayer MoS2} as explored in this article. We alsoinvestigate the electronic tunneling properties of silicene in Josephonjunction with the electric-field-induced Rashba-coupling, the anomalous effectdue to the Berry phase is mentioned. Our results is meaningful to theapplication of the spintronics and valleytronics base on the silicene-liketopological insulators.

Electronic transport and the related anomalous effects in silicene-like hexagonal lattice