Direct current generation by dielectric loss in ferroelectrics

We study direct current (DC) generation induced by microwave irradiation to ferroelectric materials. The DC generation originates from microwave absorption called dielectric loss due to the delay of dielectric response. Such current generation can be formulated as the low-frequency limit of the phonon shift current which arises from an increase of electric polarization accompanying photoexcitation of phonons due to the electron-phonon coupling. To study the DC generation by the dielectric loss, we apply the diagrammatic treatment of nonlinear optical responses to photoexcitations of phonons and derive the general formula for phonon shift current. We then study the DC generation in the low-frequency region and find that the current scales as $\propto \omega^2$ for the linearly polarized light and time reversal symmetric systems. We estimate the order of magnitude of the DC generation by dielectric loss, indicating its feasibility for experimental detection in the GHz region.