We theoretically study the effect of the Berry curvature on the transport properties of Weyl semimetals using a semiclassical Boltzmann transport theory, which results in nonlinear optical responses. In the adiabatic process, the Berry curvature, which involves the time derivative of the Bloch states, contributes to the transport properties such as the adiabatic Thouless pump. Although this effect is very weak in usual solids, it is enhanced in Weyl semimetals, where the Berry curvature contributes to observable nonlinear optical responses due to its nodal structure. In this paper, using the semiclassical Boltzmann theory, we show that a dc photocurrent induced by the Berry curvature robustly persists even in the limit of short scattering time. We also show that the photocurrent is well explained as a consequence of the electromagnetic induction in momentum space. The results indicate that the electromagnetic induction gives rise to a nondissipative photocurrent that is robust against decoherence within a time scale shorter than the periodicity of the incident electromagnetic field. We also discuss the second harmonic response of an ac current when the electron distribution is displaced from the ground state by an external field.
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