  We investigate the anomalous effects due to the Berry correction and the
considerable perturbations in the silicene-like hexagonal lattice system. The
Berry curvature in periodic Bloch band system which related to the
electromagnetic field is explored, the induced transverse anomalous velocity
gives rise to the intrinsic Hall conductivity (without the vertex correction)
expecially in the quantum anomalous Hall phase. The quantum anomalous Hall
effect which related to the anomalous velocity term is detected, including the
band avoided corssing effect and the generated special band gap. %{Enlarged
Galilean symmetry of anyons and the Hall effect} The topological spin transport
is affected by the Berry curvature %{Topological spin transport of a
relativistic electron} %{Anomalous direction for skyrmion bubble motion} and
the spin-current-induced Skyrmion spin texture motion is contrasted between the
quantum spin Hall effect and quantum anomalous Hall effect. Since silicene
involving the orbital degree of freedom, the orbital magnetic moment and
orbital magnetization contributes significantly to the electronic transport
properties of silicene %{Photoinduced quantum spin and valley Hall effects, and
orbital magnetization in monolayer MoS2} as explored in this article. We also
investigate the electronic tunneling properties of silicene in Josephon
junction with the electric-field-induced Rashba-coupling, the anomalous effect
due to the Berry phase is mentioned. Our results is meaningful to the
application of the spintronics and valleytronics base on the silicene-like
topological insulators.
