Abstract: Periodic potential and Bloch^,s theorem in solid makes Berry curvature different from that in continuousmedia. The Bloch wave function of the n-th energy band at k point in Brillouin zone has its modulation factor unk(r), and the corresponding Berry curvature is given by Ωnk=×Ank with Berry connection Ank=〈unk|ik|unk〉. In the presence of inversion and time reversal symmetries, Berry curvature vanishes at in any k point of Brillouin zone. With broken inversion and time reversal symmetries, or with spin-orbit coupling, or the band degeneracy, Berry curvature can be nonzero. Berry curvature induces an anomalous velocity perpendicular to external electric field, which in turn leads to the intrinsic anomalous Hall effect, the intrinsic spin Hall effect and the nonlinear Hall effect. This work is helpful for a better understanding of Bloch wave function and Boltzmann transport equation.

Key words: Berry phase, Berry curvature, Bloch function, anomalous velocity