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Semiclassical theory of the circular photogalvanic effect in gyrotropic systems

We develop a theory of circular photogalvanic effect (CPGE) for classically high photon energies which exceed the electron scattering rate but are small compared to the average electron kinetic energy. In this frequency range one can calculate the CPGE by using two different approaches. In the fully quantum-mechanical approach we find the photocurrent density by applying Fermi's golden rule for indirect intraband optical transitions with virtual intermediate states both in the conduction and valence bands. In the framework of the semiclassical approach, we apply a generalized Boltzmann equation with accounts for the Berry-curvature induced anomalous velocity, side jumps and skew scattering. The calculation is carried out for a wurtzite symmetry crystal. Both methods yield the same results for the CPGE current demonstrating consistency between the two approaches and applicability of the semiclassical theory for the description of nonlinear high-frequency transport.