We develop a semiclassical theory of nonlinear transport and the photogalvanic effect in non-centrosymmetric media. We show that terms in semiclassical kinetic equations for electron motion which are associated with the Berry curvature and side jumps give rise to a dc current quadratic in the amplitude of the ac electric field. We demonstrate that the circular photogalvanic effect is governed by these terms in contrast to the linear photogalvanic effect and nonlinear I-V characteristics which are governed mainly by the skew scattering mechanism. In addition, the Berry curvature contribution to the magnetic-field induced photogalvanic effect is calculated.
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