The Rabbi Limit of Current Rectification in Solids

We investigate rectified currents in response to oscillating electric fields in materials lacking inversion and time-reversal symmetries, which in second-order perturbation theory are inversely proportional to the relaxation rate, and, therefore, naively diverge in the ideal clean limit. Employing a combination of the Keldysh technique and Floquet theory, we show that this is an artefact of perturbation theory and that there is a well-defined periodic steady-state akin to Rabbi oscillations leading to finite rectified currents in the clean limit. In this Rabbi regime, the rectified current would scale as the square root of the radiation intensity, in contrast with the linear scaling expected in the perturbative regime, allowing to detect it in experiments readily. More generally, our description provides a smooth interpolation from the ideal isolated Periodic Gibbs Ensemble describing the Rabbi oscillations in the clean limit to the perturbative regime of rapid relaxation due to strong coupling to a thermal bath.